some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -925,6 +925,40 @@\n rest\n value\n \n+private theorem runtimeStateMatchesIR_writeTransientTarget\n+ {fields : List Field}\n+ {runtime : SourceSemantics.RuntimeState}\n+ {state : IRState}\n+ {target value : Nat}\n+ (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n+ (hvalue : value < Verity.Core.Uint256.modulus) :\n+ FunctionBody.runtimeStateMatchesIR fields\n+ { runtime with\n+ world := SourceSemantics.writeTransientTargets runtime.world [target] value }\n+ { state with\n+ transientStorage := fun slot =>\n+ if slot = SourceSemantics.wordNormalize target then value else state.transientStorage slot } := by\n+ rcases hruntime with\n+ ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n+ refine ⟨?_, ?_, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n+ · funext query\n+ rw [hstorage]\n+ exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n+ (SourceSemantics.encodeStorageAt_congr (by simp [SourceSemantics.writeTransientTargets])\n+ (by simp [SourceSemantics.writeTransientTargets])\n+ (by simp [SourceSemantics.writeTransientTargets]))\n+ · funext slot\n+ by_cases hslot : slot = SourceSemantics.wordNormalize target\n+ · subst hslot\n+ simp [SourceSemantics.writeTransientTargets]\n+ exact (Nat.mod_eq_of_lt (by\n+ simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n+ Verity.Core.Uint256.modulus] using hvalue)).symm\n+ · simp [SourceSemantics.writeTransientTargets, hslot]\n+ have hslot' : slot ≠ target % Compiler.Constants.evmModulus := by\n+ simpa [SourceSemantics.wordNormalize] using hslot\n+ simp [hslot', congrFun htransient slot]\n+\n private theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n@@ -2468,7 +2502,11 @@\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n- exact ⟨by sorry,\n+ exact ⟨by\n+ simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n+ SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\n+ (runtimeStateMatchesIR_writeTransientTarget\n+ (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21332,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_59"},"challenge_id":{"kind":"string","value":"39e1e7e9f35c9887"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":59,"string":"59"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat (mapping2WordTargetSlot slot key1 key2 wordOffset)\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) =\n (runtime.world.storage (mapping2WordTargetSlot slot key1 key2 wordOffset)).val := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved, hdyn]\n simp only [hstorage, henc]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize,\n mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n SourceSemantics.wordNormalize_idem, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world)\n (slot := slot) (key1 := key1) (key2 := key2) (wordOffset := wordOffset)\n (value := value) hresolved hdyn hvalue).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key1 := key1)\n (key2 := key2) (wordOffset := wordOffset) (query := query.toNat) (value := value)\n (by simpa [mapping2WordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm","n_chars":1895,"n_subproofs":1,"n_tactics":31,"cyclomatic":2,"n_automation":5,"n_rewrites":5,"n_structural":5,"automation_only":false,"max_nesting":12}],"string":"[\n {\n \"theorem_name\": \"runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases hruntime with\\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\\n funext query\\n by_cases hEq : query = IRStorageSlot.ofNat (mapping2WordTargetSlot slot key1 key2 wordOffset)\\n · subst hEq\\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\\n have henc : SourceSemantics.encodeStorageAt fields runtime.world\\n (mapping2WordTargetSlot slot key1 key2 wordOffset) =\\n (runtime.world.storage (mapping2WordTargetSlot slot key1 key2 wordOffset)).val := by\\n rw [encodeStorageAt_eq_copy]\\n simp only [encodeStorageAtCopy, hresolved, hdyn]\\n simp only [hstorage, henc]\\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize,\\n mapping2WordTargetSlot, SourceSemantics.wordNormalize,\\n SourceSemantics.wordNormalize_idem, Compiler.Constants.evmModulus,\\n Verity.Core.UINT256_MODULUS] using\\n (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\\n (fields := fields) (world := runtime.world)\\n (slot := slot) (key1 := key1) (key2 := key2) (wordOffset := wordOffset)\\n (value := value) hresolved hdyn hvalue).symm)\\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\\n simp only [hEq, ↓reduceIte]\\n rw [hstorage]\\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\\n (fields := fields) (world := runtime.world) (slot := slot) (key1 := key1)\\n (key2 := key2) (wordOffset := wordOffset) (query := query.toNat) (value := value)\\n (by simpa [mapping2WordTargetSlot] using\\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\",\n \"n_chars\": 1895,\n \"n_subproofs\": 1,\n \"n_tactics\": 31,\n \"cyclomatic\": 2,\n \"n_automation\": 5,\n \"n_rewrites\": 5,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 12\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other","text":"private theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset query value : Nat}\n (hneq :\n query ≠ mapping2WordTargetSlot slot key1 key2 wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq :\n query =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mapping2WordTargetSlot slot key1 key2 wordOffset := by\n rw [mapping2WordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 %\n Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)\n wordOffset Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n\n","fan_in":1,"n_lines":50,"n_chars":2364,"n_subproofs":2,"n_tactics":39,"cyclomatic":1,"n_automation":3,"n_rewrites":3,"n_structural":6,"automation_only":false,"max_nesting":18}],"string":"[\n {\n \"name\": \"encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\",\n \"text\": \"private theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\\n {fields : List Field}\\n {world : Verity.ContractState}\\n {slot key1 key2 wordOffset query value : Nat}\\n (hneq :\\n query ≠ mapping2WordTargetSlot slot key1 key2 wordOffset) :\\n SourceSemantics.encodeStorageAt fields\\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\\n query =\\n SourceSemantics.encodeStorageAt fields world query := by\\n apply SourceSemantics.encodeStorageAt_congr\\n · by_cases hEq :\\n query =\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\\n Compiler.Constants.evmModulus\\n · exfalso\\n have htarget : query = mapping2WordTargetSlot slot key1 key2 wordOffset := by\\n rw [mapping2WordTargetSlot_eq_uint256_add]\\n have hslotEq :\\n (Verity.Core.Uint256.ofNat wordOffset +\\n Verity.Core.Uint256.ofNat\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val =\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\\n Compiler.Constants.evmModulus := by\\n change\\n (wordOffset % Compiler.Constants.evmModulus +\\n Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 %\\n Compiler.Constants.evmModulus) %\\n Compiler.Constants.evmModulus =\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\\n Compiler.Constants.evmModulus\\n rw [Nat.add_comm]\\n exact (Nat.add_mod\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)\\n wordOffset Compiler.Constants.evmModulus).symm\\n exact hEq.trans hslotEq.symm\\n exact hneq htarget\\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, List.map_cons, List.map_nil]\\n intro hbad\\n exact False.elim (hEq hbad)\\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 50,\n \"n_chars\": 2364,\n \"n_subproofs\": 2,\n \"n_tactics\": 39,\n \"cyclomatic\": 1,\n \"n_automation\": 3,\n \"n_rewrites\": 3,\n \"n_structural\": 6,\n \"automation_only\": false,\n \"max_nesting\": 18\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves","fan_in":1,"n_deps_direct":1,"n_deps_transitive":28,"n_lines":85,"n_chars":4957,"n_subproofs":1,"n_tactics":19,"cyclomatic":7,"n_automation":3,"n_rewrites":1,"n_structural":6,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\",\n \"fan_in\": 1,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 28,\n \"n_lines\": 85,\n \"n_chars\": 4957,\n \"n_subproofs\": 1,\n \"n_tactics\": 19,\n \"cyclomatic\": 7,\n \"n_automation\": 3,\n \"n_rewrites\": 1,\n \"n_structural\": 6,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":20,"string":"20"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\ntheorem mapping2WordTargetSlot_eq_uint256_add (slot key1 key2 wordOffset : Nat) :\n mapping2WordTargetSlot slot key1 key2 wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val := by\n unfold mapping2WordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\ntheorem findDynamicArrayElementAtSlotCopy_scanElements_wordNormalize\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy.scanElements\n (SourceSemantics.wordNormalize targetSlot) baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons _ rest ih =>\n simp only [findDynamicArrayElementAtSlotCopy.scanElements]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n\ntheorem findDynamicArrayElementAtSlotCopy_go_wordNormalize\n (remaining : List Field) (world : Verity.ContractState) (idx targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy.go world (SourceSemantics.wordNormalize targetSlot)\n remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [findDynamicArrayElementAtSlotCopy.go]\n rw [findDynamicArrayElementAtSlotCopy_scanElements_wordNormalize]\n split\n · split\n · rfl\n · exact ih (idx + 1)\n · exact ih (idx + 1)\n\ntheorem findDynamicArrayElementAtSlotCopy_wordNormalize\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy fields world (SourceSemantics.wordNormalize targetSlot) =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset value : Nat}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = value := by\n rw [encodeStorageAt_eq_copy]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = none := by\n rw [findResolvedFieldAtSlotCopy_wordNormalize]\n exact hresolved\n simp only [encodeStorageAtCopy, hresolved']\n have harray : (SourceSemantics.writeAddressKeyedMapping2WordSlots\n world [slot] key1 key2 wordOffset value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset))\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset))\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2]\n rw [findDynamicArrayElementAtSlotCopy_wordNormalize]\n exact hdyn\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, mapping2WordTargetSlot,\n SourceSemantics.wordNormalize, Verity.Core.Uint256.val_ofNat]\n have htargetLt :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).isLt\n simp [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n htargetLt, Nat.mod_eq_of_lt hvalue]\n simpa [Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using hvalue\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeTransientTarget\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {target value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeTransientTargets runtime.world [target] value }\n { state with\n transientStorage := fun slot =>\n if slot = SourceSemantics.wordNormalize target then value else state.transientStorage slot } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, ?_, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr (by simp [SourceSemantics.writeTransientTargets])\n (by simp [SourceSemantics.writeTransientTargets])\n (by simp [SourceSemantics.writeTransientTargets]))\n · funext slot\n by_cases hslot : slot = SourceSemantics.wordNormalize target\n · subst hslot\n simp [SourceSemantics.writeTransientTargets]\n exact (Nat.mod_eq_of_lt (by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Verity.Core.Uint256.modulus] using hvalue)).symm\n · simp [SourceSemantics.writeTransientTargets, hslot]\n have hslot' : slot ≠ target % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hslot\n simp [hslot', congrFun htransient slot]\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot key1 key2 wordOffset value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1 key2 wordOffset value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mapping2WordTargetSlot slot key1 key2 wordOffset)\n value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat (mapping2WordTargetSlot slot key1 key2 wordOffset)\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) =\n (runtime.world.storage (mapping2WordTargetSlot slot key1 key2 wordOffset)).val := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved, hdyn]\n simp only [hstorage, henc]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize,\n mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n SourceSemantics.wordNormalize_idem, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world)\n (slot := slot) (key1 := key1) (key2 := key2) (wordOffset := wordOffset)\n (value := value) hresolved hdyn hvalue).symm)\n · sorry\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem evalIRExpr_mappingSlot2_of_eval\n {state : IRState} {slot key1Nat key2Nat : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [key1IR, key2IR])\n (keyVals := [key1Nat, key2Nat])\n (by simp [hkey1, hkey2] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [key1IR, key2IR] [key1Nat, key2Nat]))\n\nprivate theorem evalIRExpr_mappingSlot2_add_of_eval\n {state : IRState} {slot key1Nat key2Nat wordOffset : Nat}\n {key1IR key2IR : YulExpr}\n (hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)) :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR],\n YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) := by\n have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n (b := wordOffset)\n hMappingSlot2Eval\n (by simp [evalIRExpr])\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc,\n Nat.add_comm, Nat.add_left_comm] using hAddEval\n\nprivate theorem evalIRExpr_mapping2WordTarget_of_eval\n {state : IRState} {slot key1Nat key2Nat wordOffset : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIRExpr state\n (let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]) =\n some (mapping2WordTargetSlot slot key1Nat key2Nat wordOffset) := by\n have hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat) :=\n evalIRExpr_mappingSlot2_of_eval hkey1 hkey2\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat <\n Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n simpa [mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.mod_eq_of_lt hlt] using\n hMappingSlot2Eval\n · have hAddEval' :=\n evalIRExpr_mappingSlot2_add_of_eval\n (wordOffset := wordOffset)\n hMappingSlot2Eval\n simpa [hzero, mapping2WordTargetSlot_eq_uint256_add] using hAddEval'\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key1 key2 value : Expr}\n {wordOffset : Nat}\n {key1IR key2IR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey1 : FunctionBody.ExprCompileCore key1)\n (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2)\n (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] -\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime (.setMapping2Word fieldName key1 key2 wordOffset value) =\n sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])]\n -- Evaluate key1 expression\n have hkey1SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey1 hexact hinScopeKey1 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey1)\n hruntime\n rw [hkey1IR] at hkey1SourceEval\n simp [Except.toOption] at hkey1SourceEval\n rcases hIRKey1 : evalIRExpr state key1IR with _ | key1Nat\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n -- Evaluate key2 expression\n have hkey2SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey2 hexact hinScopeKey2 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey2)\n hruntime\n rw [hkey2IR] at hkey2SourceEval\n simp [Except.toOption] at hkey2SourceEval\n rcases hIRKey2 : evalIRExpr state key2IR with _ | key2Nat\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n -- Evaluate value expression\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKey1Src : SourceSemantics.evalExpr fields runtime key1 = some key1Nat :=\n hkey1SourceEval.symm\n have hKey2Src : SourceSemantics.evalExpr fields runtime key2 = some key2Nat :=\n hkey2SourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime key1Nat key2Nat hKey1Src hKey2Src with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set targetSlot := mapping2WordTargetSlot slot key1Nat key2Nat wordOffset\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n simpa [writeSlotExpr, targetSlot] using\n (evalIRExpr_mapping2WordTarget_of_eval\n (state := state) (slot := slot) (wordOffset := wordOffset) hIRKey1 hIRKey2)\n have hTargetAdd :\n targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val := by\n simpa [targetSlot] using\n mapping2WordTargetSlot_eq_uint256_add slot key1Nat key2Nat wordOffset\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [hTargetAdd]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).symm\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk1 | hk2 | hv | hs\n · exact hinScopeKey1 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey1 n hk1)\n · exact hinScopeKey2 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey2 n hk2)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target :=\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordFieldSlots\n fields fieldName runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htrans, state', target, hTargetMod] using\n (execIRStmt_tstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n have htargetSlotNorm :\n targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage targetSlot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, SourceSemantics.writeAddressKeyedMapping2WordSlots,\n htransFalse, hTargetMod, htargetSlotNorm]\n have hStoreEq :\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot valueNat =\n fun s =>\n if s =\n IRStorageSlot.ofNat\n ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat valueNat\n else\n state.storage s := by\n funext s\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hTargetAdd]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htransFalse, state'] using\n (execIRStmt_sstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩\n\nprivate theorem compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\n {fields : List Field} {scope : List String}\n {fieldName memberName : String} {key1 key2 value : Expr}\n {wordOffset : Nat} {members : List StructMember}\n {key1IR key2IR valueIR : YulExpr} {slot : Nat}\n (hcoreKey1 : FunctionBody.ExprCompileCore key1)\n (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2)\n (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hmembers : findStructMembers fields fieldName = some members)\n (hmember : findStructMember members memberName =\n some { name := memberName, wordOffset := wordOffset, packed := none })\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] -\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setStructMember2 fieldName key1 key2 memberName value) = sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setStructMember2 fieldName key1 key2 memberName value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n obtain ⟨sourceResult, irExec, hSrcMappingWord, hIRExec, hmatch⟩ :=\n compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\n runtime state extraFuel hexact hscope hbounded hruntime hslack\n refine ⟨sourceResult, irExec, ?_, hIRExec, ?_⟩\n · rw [← hSrcMappingWord]\n simp only [SourceSemantics.execStmt, hwriteSlots, hmembers]\n cases SourceSemantics.evalExpr fields runtime key1 <;>\n cases SourceSemantics.evalExpr fields runtime key2 <;>\n cases SourceSemantics.evalExpr fields runtime value <;>\n simp [hmember]\n · simpa [stmtStepMatchesIRExec, stmtNextScope, collectStmtNames]\n using hmatch\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\ntheorem mapping2WordTargetSlot_eq_uint256_add (slot key1 key2 wordOffset : Nat) :\n mapping2WordTargetSlot slot key1 key2 wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val := by\n unfold mapping2WordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\ntheorem findDynamicArrayElementAtSlotCopy_scanElements_wordNormalize\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy.scanElements\n (SourceSemantics.wordNormalize targetSlot) baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons _ rest ih =>\n simp only [findDynamicArrayElementAtSlotCopy.scanElements]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n\ntheorem findDynamicArrayElementAtSlotCopy_go_wordNormalize\n (remaining : List Field) (world : Verity.ContractState) (idx targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy.go world (SourceSemantics.wordNormalize targetSlot)\n remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [findDynamicArrayElementAtSlotCopy.go]\n rw [findDynamicArrayElementAtSlotCopy_scanElements_wordNormalize]\n split\n · split\n · rfl\n · exact ih (idx + 1)\n · exact ih (idx + 1)\n\ntheorem findDynamicArrayElementAtSlotCopy_wordNormalize\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy fields world (SourceSemantics.wordNormalize targetSlot) =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset query value : Nat}\n (hneq :\n query ≠ mapping2WordTargetSlot slot key1 key2 wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq :\n query =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mapping2WordTargetSlot slot key1 key2 wordOffset := by\n rw [mapping2WordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 %\n Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)\n wordOffset Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset value : Nat}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = value := by\n rw [encodeStorageAt_eq_copy]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = none := by\n rw [findResolvedFieldAtSlotCopy_wordNormalize]\n exact hresolved\n simp only [encodeStorageAtCopy, hresolved']\n have harray : (SourceSemantics.writeAddressKeyedMapping2WordSlots\n world [slot] key1 key2 wordOffset value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset))\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset))\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2]\n rw [findDynamicArrayElementAtSlotCopy_wordNormalize]\n exact hdyn\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, mapping2WordTargetSlot,\n SourceSemantics.wordNormalize, Verity.Core.Uint256.val_ofNat]\n have htargetLt :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).isLt\n simp [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n htargetLt, Nat.mod_eq_of_lt hvalue]\n simpa [Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using hvalue\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeTransientTarget\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {target value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeTransientTargets runtime.world [target] value }\n { state with\n transientStorage := fun slot =>\n if slot = SourceSemantics.wordNormalize target then value else state.transientStorage slot } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, ?_, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr (by simp [SourceSemantics.writeTransientTargets])\n (by simp [SourceSemantics.writeTransientTargets])\n (by simp [SourceSemantics.writeTransientTargets]))\n · funext slot\n by_cases hslot : slot = SourceSemantics.wordNormalize target\n · subst hslot\n simp [SourceSemantics.writeTransientTargets]\n exact (Nat.mod_eq_of_lt (by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Verity.Core.Uint256.modulus] using hvalue)).symm\n · simp [SourceSemantics.writeTransientTargets, hslot]\n have hslot' : slot ≠ target % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hslot\n simp [hslot', congrFun htransient slot]\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot key1 key2 wordOffset value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1 key2 wordOffset value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mapping2WordTargetSlot slot key1 key2 wordOffset)\n value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat (mapping2WordTargetSlot slot key1 key2 wordOffset)\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) =\n (runtime.world.storage (mapping2WordTargetSlot slot key1 key2 wordOffset)).val := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved, hdyn]\n simp only [hstorage, henc]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize,\n mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n SourceSemantics.wordNormalize_idem, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world)\n (slot := slot) (key1 := key1) (key2 := key2) (wordOffset := wordOffset)\n (value := value) hresolved hdyn hvalue).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key1 := key1)\n (key2 := key2) (wordOffset := wordOffset) (query := query.toNat) (value := value)\n (by simpa [mapping2WordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem evalIRExpr_mappingSlot2_of_eval\n {state : IRState} {slot key1Nat key2Nat : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [key1IR, key2IR])\n (keyVals := [key1Nat, key2Nat])\n (by simp [hkey1, hkey2] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [key1IR, key2IR] [key1Nat, key2Nat]))\n\nprivate theorem evalIRExpr_mappingSlot2_add_of_eval\n {state : IRState} {slot key1Nat key2Nat wordOffset : Nat}\n {key1IR key2IR : YulExpr}\n (hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)) :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR],\n YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) := by\n have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n (b := wordOffset)\n hMappingSlot2Eval\n (by simp [evalIRExpr])\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc,\n Nat.add_comm, Nat.add_left_comm] using hAddEval\n\nprivate theorem evalIRExpr_mapping2WordTarget_of_eval\n {state : IRState} {slot key1Nat key2Nat wordOffset : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIRExpr state\n (let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]) =\n some (mapping2WordTargetSlot slot key1Nat key2Nat wordOffset) := by\n have hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat) :=\n evalIRExpr_mappingSlot2_of_eval hkey1 hkey2\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat <\n Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n simpa [mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.mod_eq_of_lt hlt] using\n hMappingSlot2Eval\n · have hAddEval' :=\n evalIRExpr_mappingSlot2_add_of_eval\n (wordOffset := wordOffset)\n hMappingSlot2Eval\n simpa [hzero, mapping2WordTargetSlot_eq_uint256_add] using hAddEval'\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key1 key2 value : Expr}\n {wordOffset : Nat}\n {key1IR key2IR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey1 : FunctionBody.ExprCompileCore key1)\n (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2)\n (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] -\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime (.setMapping2Word fieldName key1 key2 wordOffset value) =\n sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])]\n -- Evaluate key1 expression\n have hkey1SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey1 hexact hinScopeKey1 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey1)\n hruntime\n rw [hkey1IR] at hkey1SourceEval\n simp [Except.toOption] at hkey1SourceEval\n rcases hIRKey1 : evalIRExpr state key1IR with _ | key1Nat\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n -- Evaluate key2 expression\n have hkey2SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey2 hexact hinScopeKey2 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey2)\n hruntime\n rw [hkey2IR] at hkey2SourceEval\n simp [Except.toOption] at hkey2SourceEval\n rcases hIRKey2 : evalIRExpr state key2IR with _ | key2Nat\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n -- Evaluate value expression\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKey1Src : SourceSemantics.evalExpr fields runtime key1 = some key1Nat :=\n hkey1SourceEval.symm\n have hKey2Src : SourceSemantics.evalExpr fields runtime key2 = some key2Nat :=\n hkey2SourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime key1Nat key2Nat hKey1Src hKey2Src with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set targetSlot := mapping2WordTargetSlot slot key1Nat key2Nat wordOffset\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n simpa [writeSlotExpr, targetSlot] using\n (evalIRExpr_mapping2WordTarget_of_eval\n (state := state) (slot := slot) (wordOffset := wordOffset) hIRKey1 hIRKey2)\n have hTargetAdd :\n targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val := by\n simpa [targetSlot] using\n mapping2WordTargetSlot_eq_uint256_add slot key1Nat key2Nat wordOffset\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [hTargetAdd]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).symm\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk1 | hk2 | hv | hs\n · exact hinScopeKey1 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey1 n hk1)\n · exact hinScopeKey2 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey2 n hk2)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target :=\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordFieldSlots\n fields fieldName runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htrans, state', target, hTargetMod] using\n (execIRStmt_tstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n have htargetSlotNorm :\n targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage targetSlot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, SourceSemantics.writeAddressKeyedMapping2WordSlots,\n htransFalse, hTargetMod, htargetSlotNorm]\n have hStoreEq :\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot valueNat =\n fun s =>\n if s =\n IRStorageSlot.ofNat\n ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat valueNat\n else\n state.storage s := by\n funext s\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hTargetAdd]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htransFalse, state'] using\n (execIRStmt_sstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩\n\nprivate theorem compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\n {fields : List Field} {scope : List String}\n {fieldName memberName : String} {key1 key2 value : Expr}\n {wordOffset : Nat} {members : List StructMember}\n {key1IR key2IR valueIR : YulExpr} {slot : Nat}\n (hcoreKey1 : FunctionBody.ExprCompileCore key1)\n (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2)\n (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hmembers : findStructMembers fields fieldName = some members)\n (hmember : findStructMember members memberName =\n some { name := memberName, wordOffset := wordOffset, packed := none })\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] -\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setStructMember2 fieldName key1 key2 memberName value) = sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setStructMember2 fieldName key1 key2 memberName value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n obtain ⟨sourceResult, irExec, hSrcMappingWord, hIRExec, hmatch⟩ :=\n compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\n runtime state extraFuel hexact hscope hbounded hruntime hslack\n refine ⟨sourceResult, irExec, ?_, hIRExec, ?_⟩\n · rw [← hSrcMappingWord]\n simp only [SourceSemantics.execStmt, hwriteSlots, hmembers]\n cases SourceSemantics.evalExpr fields runtime key1 <;>\n cases SourceSemantics.evalExpr fields runtime key2 <;>\n cases SourceSemantics.evalExpr fields runtime value <;>\n simp [hmember]\n · simpa [stmtStepMatchesIRExec, stmtNextScope, collectStmtNames]\n using hmatch\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -802,6 +802,55 @@\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n \n+private theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n+ {fields : List Field}\n+ {world : Verity.ContractState}\n+ {slot key1 key2 wordOffset query value : Nat}\n+ (hneq :\n+ query ≠ mapping2WordTargetSlot slot key1 key2 wordOffset) :\n+ SourceSemantics.encodeStorageAt fields\n+ (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n+ query =\n+ SourceSemantics.encodeStorageAt fields world query := by\n+ apply SourceSemantics.encodeStorageAt_congr\n+ · by_cases hEq :\n+ query =\n+ (Compiler.Proofs.solidityMappingSlot\n+ (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n+ Compiler.Constants.evmModulus\n+ · exfalso\n+ have htarget : query = mapping2WordTargetSlot slot key1 key2 wordOffset := by\n+ rw [mapping2WordTargetSlot_eq_uint256_add]\n+ have hslotEq :\n+ (Verity.Core.Uint256.ofNat wordOffset +\n+ Verity.Core.Uint256.ofNat\n+ (Compiler.Proofs.solidityMappingSlot\n+ (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val =\n+ (Compiler.Proofs.solidityMappingSlot\n+ (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n+ Compiler.Constants.evmModulus := by\n+ change\n+ (wordOffset % Compiler.Constants.evmModulus +\n+ Compiler.Proofs.solidityMappingSlot\n+ (Compiler.Proofs.solidityMappingSlot slot key1) key2 %\n+ Compiler.Constants.evmModulus) %\n+ Compiler.Constants.evmModulus =\n+ (Compiler.Proofs.solidityMappingSlot\n+ (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n+ Compiler.Constants.evmModulus\n+ rw [Nat.add_comm]\n+ exact (Nat.add_mod\n+ (Compiler.Proofs.solidityMappingSlot\n+ (Compiler.Proofs.solidityMappingSlot slot key1) key2)\n+ wordOffset Compiler.Constants.evmModulus).symm\n+ exact hEq.trans hslotEq.symm\n+ exact hneq htarget\n+ · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, List.map_cons, List.map_nil]\n+ intro hbad\n+ exact False.elim (hEq hbad)\n+ · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n+ · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n+\n private theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n@@ -1020,7 +1069,14 @@\n (fields := fields) (world := runtime.world)\n (slot := slot) (key1 := key1) (key2 := key2) (wordOffset := wordOffset)\n (value := value) hresolved hdyn hvalue).symm)\n- · sorry\n+ · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n+ simp only [hEq, ↓reduceIte]\n+ rw [hstorage]\n+ exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n+ (fields := fields) (world := runtime.world) (slot := slot) (key1 := key1)\n+ (key2 := key2) (wordOffset := wordOffset) (query := query.toNat) (value := value)\n+ (by simpa [mapping2WordTargetSlot] using\n+ IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n \n private theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21333,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_60"},"challenge_id":{"kind":"string","value":"1f330491ac5d1a12"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":60,"string":"60"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":6,"string":"6"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves","depth":1,"n_commands":0,"n_lines":142,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], valueIR])]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n -- Case split on IR eval results to extract concrete Nat values\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Scope inclusion: stmtNextScope only adds expr names already in scope\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingUint fieldName key value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingUint fieldName key value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target := SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot keyNat)\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintKeyedMappingFieldSlots\n fields fieldName runtime.world [slot] keyNat valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingUint fieldName key value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\n SourceSemantics.writeUintKeyedMappingFieldSlots, htrans, target]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], valueIR])) =\n .continue state' := by\n have htargetMod :\n Compiler.Proofs.solidityMappingSlot slot keyNat %\n Compiler.Constants.evmModulus =\n Compiler.Proofs.solidityMappingSlot slot keyNat := by\n exact Nat.mod_eq_of_lt (by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat))\n simp [execIRStmt, evalIRExpr, evalIRCall, evalIRExprs, hIRKey, hIRValue,\n fieldStoreBuiltin, htrans, target, state', htargetMod,\n Compiler.Proofs.abstractMappingSlot_eq_solidity,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingUint fieldName key value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingUint fieldName key value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeUintKeyedMappingFieldSlots,\n htrans, target] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreMappingEntry\n state.storage slot keyNat valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintKeyedMappingSlots\n runtime.world [slot] keyNat valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingUint fieldName key value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\n SourceSemantics.writeUintKeyedMappingFieldSlots, htransFalse]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], valueIR])) =\n .continue state' := by\n simp [execIRStmt, evalIRExpr, hIRKey, hIRValue, fieldStoreBuiltin,\n htransFalse, Compiler.Proofs.abstractStoreMappingEntry_eq, state']\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingUint fieldName key value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeMappingSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingUint fieldName key value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintKeyedMappingSlot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩","n_chars":8075,"n_subproofs":21,"n_tactics":141,"cyclomatic":7,"n_automation":23,"n_rewrites":3,"n_structural":17,"automation_only":false,"max_nesting":18},{"theorem_name":"compiledStmtStep_setMappingChain_singleSlot_of_slotSafety_preserves","depth":1,"n_commands":0,"n_lines":161,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit slot)\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])]\n -- Evaluate value expression\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n -- Evaluate key list expressions\n rcases eval_compileExprList_core_of_scope\n hcoreKeys hexact hinScopeKeys hbounded hscope hruntime hkeyIRs with\n ⟨resolvedKeys, hkeysEval, hkeyIRVals⟩\n -- Slot safety\n rcases hslotSafety runtime resolvedKeys hkeysEval with\n ⟨hresolvedNone, hdynNone⟩\n -- Compute the foldl slot expression\n have hWriteSlotEval :\n evalIRExpr state writeSlotExpr =\n some (SourceSemantics.mappingSlotChain slot resolvedKeys) :=\n evalIRExpr_mappingSlotChain hkeyIRVals\n -- Value boundedness\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingChain fieldName keys value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · -- name from collectExprListNames keys — prove ∃ expr ∈ keys with name ∈ collectExprNames expr\n suffices ∀ (ks : List Expr),\n (∀ e, e ∈ ks → FunctionBody.ExprCompileCore e) →\n (∀ e, e ∈ ks → FunctionBody.exprBoundNamesInScope e scope) →\n n ∈ collectExprListNames ks → n ∈ scope from\n this keys hcoreKeys hinScopeKeys hk\n intro ks hcore' hscope' hmem\n induction ks with\n | nil => simp [collectExprListNames] at hmem\n | cons hd tl ih =>\n simp [collectExprListNames] at hmem\n rcases hmem with hhd | htl\n · exact hscope' hd (by simp) n\n (collectExprNames_mem_exprBoundNames_of_core (hcore' hd (by simp)) n hhd)\n · exact ih (fun e he => hcore' e (by simp [he]))\n (fun e he => hscope' e (by simp [he])) htl\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingChain fieldName keys value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target := SourceSemantics.wordNormalize\n (SourceSemantics.mappingSlotChain slot resolvedKeys)\n set state' := { state with\n transientStorage := fun o =>\n if o = target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMappingChainFieldSlots\n fields fieldName runtime.world [slot] resolvedKeys valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingChain fieldName keys value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hkeysEval, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMappingChainFieldSlots, htrans, target,\n SourceSemantics.mappingSlotChain]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])) =\n .continue state' := by\n have h := execIRStmt_tstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (fuel := extraFuel) hWriteSlotEval hIRValue\n simpa [fieldStoreBuiltin, htrans, state', target, SourceSemantics.wordNormalize,\n SourceSemantics.mappingSlotChain] using h\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingChain fieldName keys value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hbounded' : FunctionBody.bindingsBounded runtime'.bindings := by\n simpa [runtime'] using hbounded\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingChain fieldName keys value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨_, _, hSrcExec, hIRExec, ?_⟩\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMappingChainFieldSlots,\n htrans, target, SourceSemantics.mappingSlotChain] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded', hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (SourceSemantics.mappingSlotChain slot resolvedKeys)\n valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMappingChainSlots\n runtime.world [slot] resolvedKeys valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingChain fieldName keys value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hkeysEval, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMappingChainFieldSlots, htransFalse]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])) =\n .continue state' := by\n simpa [fieldStoreBuiltin, htransFalse, state'] using\n (execIRStmt_sstore_foldl_mappingSlot\n (state := state) (baseSlot := slot) (keyIRs := keyIRs)\n (keyVals := resolvedKeys) (valueExpr := valueIR)\n (valueVal := valueNat) (fuel := extraFuel) hkeyIRVals hIRValue)\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingChain fieldName keys value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\n hincl\n have hbounded' : FunctionBody.bindingsBounded runtime'.bindings := by\n simpa [runtime'] using hbounded\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingChain fieldName keys value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields runtime' state' :=\n runtimeStateMatchesIR_writeAddressKeyedMappingChainSlot\n hruntime hresolvedNone hdynNone hvalueLt\n exact ⟨_, _, hSrcExec, hIRExec,\n hruntime', hexact', hbounded', hscopeRuntime'⟩","n_chars":8577,"n_subproofs":24,"n_tactics":157,"cyclomatic":9,"n_automation":26,"n_rewrites":2,"n_structural":19,"automation_only":false,"max_nesting":14},{"theorem_name":"compiledStmtStep_setMapping_singleSlot_of_slotSafety_preserves","depth":1,"n_commands":0,"n_lines":142,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], valueIR])]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n -- Case split on IR eval results to extract concrete Nat values\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Scope inclusion: stmtNextScope only adds expr names already in scope\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMapping fieldName key value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping fieldName key value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target := SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot keyNat)\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMappingFieldSlots\n fields fieldName runtime.world [slot] keyNat valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping fieldName key value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMappingFieldSlots, htrans, target]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], valueIR])) =\n .continue state' := by\n have htargetMod :\n Compiler.Proofs.solidityMappingSlot slot keyNat %\n Compiler.Constants.evmModulus =\n Compiler.Proofs.solidityMappingSlot slot keyNat := by\n exact Nat.mod_eq_of_lt (by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat))\n simp [execIRStmt, evalIRExpr, evalIRCall, evalIRExprs, hIRKey, hIRValue,\n fieldStoreBuiltin, htrans, target, state', htargetMod,\n Compiler.Proofs.abstractMappingSlot_eq_solidity,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping fieldName key value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping fieldName key value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMappingFieldSlots,\n htrans, target] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreMappingEntry\n state.storage slot keyNat valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMappingSlots\n runtime.world [slot] keyNat valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping fieldName key value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMappingFieldSlots, htransFalse]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], valueIR])) =\n .continue state' := by\n simp [execIRStmt, evalIRExpr, hIRKey, hIRValue, fieldStoreBuiltin,\n htransFalse, Compiler.Proofs.abstractStoreMappingEntry_eq, state']\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping fieldName key value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeMappingSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping fieldName key value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMappingSlot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩","n_chars":8061,"n_subproofs":21,"n_tactics":141,"cyclomatic":7,"n_automation":23,"n_rewrites":3,"n_structural":17,"automation_only":false,"max_nesting":18},{"theorem_name":"compiledStmtStep_setMappingWord_singleSlot_of_slotSafety_preserves","depth":1,"n_commands":0,"n_lines":165,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n simpa [writeSlotExpr, targetSlot] using\n (evalIRExpr_mappingWordTarget_of_eval\n (state := state) (slot := slot) (wordOffset := wordOffset) hIRKey)\n -- Scope inclusion: stmtNextScope only adds expr names already in scope\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target :=\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMappingWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingWord fieldName key wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMappingWordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htrans, state', target, hTargetMod] using\n (execIRStmt_tstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])] =\n .continue state' := by\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, ?_, ?_⟩\n · simpa [writeSlotExpr] using hIRExec\n · simp [stmtStepMatchesIRExec]\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMappingWordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n have htargetSlotNorm :\n targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage targetSlot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMappingWordSlots\n runtime.world [slot] keyNat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingWord fieldName key wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMappingWordFieldSlots,\n SourceSemantics.writeMappingTargets, SourceSemantics.writeAddressKeyedMappingWordSlots,\n htransFalse, hTargetMod, htargetSlotNorm]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htransFalse, state'] using\n (execIRStmt_sstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])] =\n .continue state' := by\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, ?_, ?_⟩\n · simpa [writeSlotExpr] using hIRExec\n · simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMappingWordSlot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩","n_chars":9423,"n_subproofs":22,"n_tactics":165,"cyclomatic":7,"n_automation":26,"n_rewrites":5,"n_structural":17,"automation_only":false,"max_nesting":18},{"theorem_name":"compiledStmtStep_setMapping2_singleSlot_of_slotSafety_preserves","depth":1,"n_commands":0,"n_lines":172,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR], valueIR])]\n -- Evaluate key1 expression\n have hkey1SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey1 hexact hinScopeKey1 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey1)\n hruntime\n rw [hkey1IR] at hkey1SourceEval\n simp [Except.toOption] at hkey1SourceEval\n rcases hIRKey1 : evalIRExpr state key1IR with _ | key1Nat\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n -- Evaluate key2 expression\n have hkey2SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey2 hexact hinScopeKey2 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey2)\n hruntime\n rw [hkey2IR] at hkey2SourceEval\n simp [Except.toOption] at hkey2SourceEval\n rcases hIRKey2 : evalIRExpr state key2IR with _ | key2Nat\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n -- Evaluate value expression\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKey1Src : SourceSemantics.evalExpr fields runtime key1 = some key1Nat :=\n hkey1SourceEval.symm\n have hKey2Src : SourceSemantics.evalExpr fields runtime key2 = some key2Nat :=\n hkey2SourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime key1Nat key2Nat hKey1Src hKey2Src with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk1 | hk2 | hv | hs\n · exact hinScopeKey1 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey1 n hk1)\n · exact hinScopeKey2 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey2 n hk2)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target := SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2FieldSlots\n fields fieldName runtime.world [slot] key1Nat key2Nat valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2 fieldName key1 key2 value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2FieldSlots, htrans, target]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR], valueIR])) =\n .continue state' := by\n have htargetMod :\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat %\n Compiler.Constants.evmModulus =\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat := by\n exact Nat.mod_eq_of_lt (by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat))\n simp [execIRStmt, evalIRExpr, evalIRCall, evalIRExprs, hIRKey1, hIRKey2, hIRValue,\n fieldStoreBuiltin, htrans, target, state', htargetMod,\n Compiler.Proofs.abstractMappingSlot_eq_solidity,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2FieldSlots,\n htrans, target] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreMappingEntry\n state.storage\n (Compiler.Proofs.abstractMappingSlot slot key1Nat)\n key2Nat\n valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2Slots\n runtime.world [slot] key1Nat key2Nat valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2 fieldName key1 key2 value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2FieldSlots, htransFalse]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR], valueIR])) =\n .continue state' := by\n simp [execIRStmt, evalIRExpr, evalIRCall, evalIRExprs, hIRKey1, hIRKey2, hIRValue,\n fieldStoreBuiltin, htransFalse,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean,\n Compiler.Proofs.abstractStoreMappingEntry_eq, state']\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeMappingSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMapping2Slot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩","n_chars":9940,"n_subproofs":23,"n_tactics":169,"cyclomatic":8,"n_automation":27,"n_rewrites":4,"n_structural":19,"automation_only":false,"max_nesting":22},{"theorem_name":"compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves","depth":1,"n_commands":0,"n_lines":210,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])]\n -- Evaluate key1 expression\n have hkey1SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey1 hexact hinScopeKey1 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey1)\n hruntime\n rw [hkey1IR] at hkey1SourceEval\n simp [Except.toOption] at hkey1SourceEval\n rcases hIRKey1 : evalIRExpr state key1IR with _ | key1Nat\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n -- Evaluate key2 expression\n have hkey2SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey2 hexact hinScopeKey2 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey2)\n hruntime\n rw [hkey2IR] at hkey2SourceEval\n simp [Except.toOption] at hkey2SourceEval\n rcases hIRKey2 : evalIRExpr state key2IR with _ | key2Nat\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n -- Evaluate value expression\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKey1Src : SourceSemantics.evalExpr fields runtime key1 = some key1Nat :=\n hkey1SourceEval.symm\n have hKey2Src : SourceSemantics.evalExpr fields runtime key2 = some key2Nat :=\n hkey2SourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime key1Nat key2Nat hKey1Src hKey2Src with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set targetSlot := mapping2WordTargetSlot slot key1Nat key2Nat wordOffset\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n simpa [writeSlotExpr, targetSlot] using\n (evalIRExpr_mapping2WordTarget_of_eval\n (state := state) (slot := slot) (wordOffset := wordOffset) hIRKey1 hIRKey2)\n have hTargetAdd :\n targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val := by\n simpa [targetSlot] using\n mapping2WordTargetSlot_eq_uint256_add slot key1Nat key2Nat wordOffset\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [hTargetAdd]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).symm\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk1 | hk2 | hv | hs\n · exact hinScopeKey1 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey1 n hk1)\n · exact hinScopeKey2 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey2 n hk2)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target :=\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordFieldSlots\n fields fieldName runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htrans, state', target, hTargetMod] using\n (execIRStmt_tstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n have htargetSlotNorm :\n targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage targetSlot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, SourceSemantics.writeAddressKeyedMapping2WordSlots,\n htransFalse, hTargetMod, htargetSlotNorm]\n have hStoreEq :\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot valueNat =\n fun s =>\n if s =\n IRStorageSlot.ofNat\n ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat valueNat\n else\n state.storage s := by\n funext s\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hTargetAdd]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htransFalse, state'] using\n (execIRStmt_sstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩","n_chars":12280,"n_subproofs":26,"n_tactics":207,"cyclomatic":8,"n_automation":28,"n_rewrites":8,"n_structural":20,"automation_only":false,"max_nesting":30}],"string":"[\n {\n \"theorem_name\": \"compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 142,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\\n let compiledIR := [YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, keyIR], valueIR])]\\n have hkeySourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreKey hexact hinScopeKey hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\\n hruntime\\n have hvalueSourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hkeyIR] at hkeySourceEval\\n rw [hvalueIR] at hvalueSourceEval\\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\\n -- Case split on IR eval results to extract concrete Nat values\\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\\n · simp [hIRKey, Option.bind] at hkeySourceEval\\n · simp [hIRKey, Option.bind] at hkeySourceEval\\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\\n hkeySourceEval.symm\\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\\n hvalueSourceEval.symm\\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\\n -- Get boundedness of valueNat\\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hValueSrc] at hvalueLt\\n simp at hvalueLt\\n -- Scope inclusion: stmtNextScope only adds expr names already in scope\\n have hincl : FunctionBody.scopeNamesIncluded\\n (stmtNextScope scope (.setMappingUint fieldName key value)) scope := by\\n intro n hn\\n simp [stmtNextScope, collectStmtNames] at hn\\n rcases hn with hk | hv | hs\\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\\n · exact hs\\n have hscope' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingUint fieldName key value))\\n runtime.bindings :=\\n FunctionBody.scopeNamesPresent_of_included hscope hincl\\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\\n · let target := SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot keyNat)\\n set state' := { state with\\n transientStorage := fun o =>\\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeUintKeyedMappingFieldSlots\\n fields fieldName runtime.world [slot] keyNat valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMappingUint fieldName key value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\\n SourceSemantics.writeUintKeyedMappingFieldSlots, htrans, target]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, keyIR], valueIR])) =\\n .continue state' := by\\n have htargetMod :\\n Compiler.Proofs.solidityMappingSlot slot keyNat %\\n Compiler.Constants.evmModulus =\\n Compiler.Proofs.solidityMappingSlot slot keyNat := by\\n exact Nat.mod_eq_of_lt (by\\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat))\\n simp [execIRStmt, evalIRExpr, evalIRCall, evalIRExprs, hIRKey, hIRValue,\\n fieldStoreBuiltin, htrans, target, state', htargetMod,\\n Compiler.Proofs.abstractMappingSlot_eq_solidity,\\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMappingUint fieldName key value))\\n runtime'.bindings state' := by\\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingUint fieldName key value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\\n simp [stmtStepMatchesIRExec]\\n exact ⟨by\\n simpa [runtime', state', SourceSemantics.writeUintKeyedMappingFieldSlots,\\n htrans, target] using\\n (runtimeStateMatchesIR_writeTransientTarget\\n (target := target) hruntime hvalueLt),\\n hexact', hbounded, hscopeRuntime'⟩\\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\\n set state' := { state with\\n storage :=\\n Compiler.Proofs.abstractStoreMappingEntry\\n state.storage slot keyNat valueNat }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeUintKeyedMappingSlots\\n runtime.world [slot] keyNat valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMappingUint fieldName key value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\\n SourceSemantics.writeUintKeyedMappingFieldSlots, htransFalse]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, keyIR], valueIR])) =\\n .continue state' := by\\n simp [execIRStmt, evalIRExpr, hIRKey, hIRValue, fieldStoreBuiltin,\\n htransFalse, Compiler.Proofs.abstractStoreMappingEntry_eq, state']\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMappingUint fieldName key value))\\n runtime'.bindings state' :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (bindingsExactlyMatchIRVarsOnScope_writeMappingSlot hexact)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingUint fieldName key value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\\n simp [stmtStepMatchesIRExec]\\n exact ⟨runtimeStateMatchesIR_writeUintKeyedMappingSlot\\n hruntime hresolvedNone hdynNone hvalueLt,\\n hexact', hbounded, hscopeRuntime'⟩\",\n \"n_chars\": 8075,\n \"n_subproofs\": 21,\n \"n_tactics\": 141,\n \"cyclomatic\": 7,\n \"n_automation\": 23,\n \"n_rewrites\": 3,\n \"n_structural\": 17,\n \"automation_only\": false,\n \"max_nesting\": 18\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingChain_singleSlot_of_slotSafety_preserves\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 161,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\\n let writeSlotExpr :=\\n keyIRs.foldl\\n (fun slotExpr keyExpr => YulExpr.call \\\"mappingSlot\\\" [slotExpr, keyExpr])\\n (YulExpr.lit slot)\\n let compiledIR := [YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])]\\n -- Evaluate value expression\\n have hvalueSourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hvalueIR] at hvalueSourceEval\\n simp [Except.toOption] at hvalueSourceEval\\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\\n hvalueSourceEval.symm\\n -- Evaluate key list expressions\\n rcases eval_compileExprList_core_of_scope\\n hcoreKeys hexact hinScopeKeys hbounded hscope hruntime hkeyIRs with\\n ⟨resolvedKeys, hkeysEval, hkeyIRVals⟩\\n -- Slot safety\\n rcases hslotSafety runtime resolvedKeys hkeysEval with\\n ⟨hresolvedNone, hdynNone⟩\\n -- Compute the foldl slot expression\\n have hWriteSlotEval :\\n evalIRExpr state writeSlotExpr =\\n some (SourceSemantics.mappingSlotChain slot resolvedKeys) :=\\n evalIRExpr_mappingSlotChain hkeyIRVals\\n -- Value boundedness\\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hValueSrc] at hvalueLt\\n simp at hvalueLt\\n -- Scope inclusion\\n have hincl : FunctionBody.scopeNamesIncluded\\n (stmtNextScope scope (.setMappingChain fieldName keys value)) scope := by\\n intro n hn\\n simp [stmtNextScope, collectStmtNames] at hn\\n rcases hn with hk | hv | hs\\n · -- name from collectExprListNames keys — prove ∃ expr ∈ keys with name ∈ collectExprNames expr\\n suffices ∀ (ks : List Expr),\\n (∀ e, e ∈ ks → FunctionBody.ExprCompileCore e) →\\n (∀ e, e ∈ ks → FunctionBody.exprBoundNamesInScope e scope) →\\n n ∈ collectExprListNames ks → n ∈ scope from\\n this keys hcoreKeys hinScopeKeys hk\\n intro ks hcore' hscope' hmem\\n induction ks with\\n | nil => simp [collectExprListNames] at hmem\\n | cons hd tl ih =>\\n simp [collectExprListNames] at hmem\\n rcases hmem with hhd | htl\\n · exact hscope' hd (by simp) n\\n (collectExprNames_mem_exprBoundNames_of_core (hcore' hd (by simp)) n hhd)\\n · exact ih (fun e he => hcore' e (by simp [he]))\\n (fun e he => hscope' e (by simp [he])) htl\\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\\n · exact hs\\n have hscope' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingChain fieldName keys value))\\n runtime.bindings :=\\n FunctionBody.scopeNamesPresent_of_included hscope hincl\\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\\n · let target := SourceSemantics.wordNormalize\\n (SourceSemantics.mappingSlotChain slot resolvedKeys)\\n set state' := { state with\\n transientStorage := fun o =>\\n if o = target then valueNat else state.transientStorage o }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMappingChainFieldSlots\\n fields fieldName runtime.world [slot] resolvedKeys valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMappingChain fieldName keys value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hkeysEval, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMappingChainFieldSlots, htrans, target,\\n SourceSemantics.mappingSlotChain]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])) =\\n .continue state' := by\\n have h := execIRStmt_tstore_of_eval\\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\\n (fuel := extraFuel) hWriteSlotEval hIRValue\\n simpa [fieldStoreBuiltin, htrans, state', target, SourceSemantics.wordNormalize,\\n SourceSemantics.mappingSlotChain] using h\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMappingChain fieldName keys value))\\n runtime'.bindings state' := by\\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\\n hincl\\n have hbounded' : FunctionBody.bindingsBounded runtime'.bindings := by\\n simpa [runtime'] using hbounded\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingChain fieldName keys value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨_, _, hSrcExec, hIRExec, ?_⟩\\n exact ⟨by\\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMappingChainFieldSlots,\\n htrans, target, SourceSemantics.mappingSlotChain] using\\n (runtimeStateMatchesIR_writeTransientTarget\\n (target := target) hruntime hvalueLt),\\n hexact', hbounded', hscopeRuntime'⟩\\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\\n set state' := { state with\\n storage :=\\n Compiler.Proofs.abstractStoreStorageOrMapping\\n state.storage\\n (SourceSemantics.mappingSlotChain slot resolvedKeys)\\n valueNat }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMappingChainSlots\\n runtime.world [slot] resolvedKeys valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMappingChain fieldName keys value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hkeysEval, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMappingChainFieldSlots, htransFalse]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])) =\\n .continue state' := by\\n simpa [fieldStoreBuiltin, htransFalse, state'] using\\n (execIRStmt_sstore_foldl_mappingSlot\\n (state := state) (baseSlot := slot) (keyIRs := keyIRs)\\n (keyVals := resolvedKeys) (valueExpr := valueIR)\\n (valueVal := valueNat) (fuel := extraFuel) hkeyIRVals hIRValue)\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMappingChain fieldName keys value))\\n runtime'.bindings state' :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\\n hincl\\n have hbounded' : FunctionBody.bindingsBounded runtime'.bindings := by\\n simpa [runtime'] using hbounded\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingChain fieldName keys value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields runtime' state' :=\\n runtimeStateMatchesIR_writeAddressKeyedMappingChainSlot\\n hruntime hresolvedNone hdynNone hvalueLt\\n exact ⟨_, _, hSrcExec, hIRExec,\\n hruntime', hexact', hbounded', hscopeRuntime'⟩\",\n \"n_chars\": 8577,\n \"n_subproofs\": 24,\n \"n_tactics\": 157,\n \"cyclomatic\": 9,\n \"n_automation\": 26,\n \"n_rewrites\": 2,\n \"n_structural\": 19,\n \"automation_only\": false,\n \"max_nesting\": 14\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping_singleSlot_of_slotSafety_preserves\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 142,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\\n let compiledIR := [YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, keyIR], valueIR])]\\n have hkeySourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreKey hexact hinScopeKey hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\\n hruntime\\n have hvalueSourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hkeyIR] at hkeySourceEval\\n rw [hvalueIR] at hvalueSourceEval\\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\\n -- Case split on IR eval results to extract concrete Nat values\\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\\n · simp [hIRKey, Option.bind] at hkeySourceEval\\n · simp [hIRKey, Option.bind] at hkeySourceEval\\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\\n hkeySourceEval.symm\\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\\n hvalueSourceEval.symm\\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\\n -- Get boundedness of valueNat\\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hValueSrc] at hvalueLt\\n simp at hvalueLt\\n -- Scope inclusion: stmtNextScope only adds expr names already in scope\\n have hincl : FunctionBody.scopeNamesIncluded\\n (stmtNextScope scope (.setMapping fieldName key value)) scope := by\\n intro n hn\\n simp [stmtNextScope, collectStmtNames] at hn\\n rcases hn with hk | hv | hs\\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\\n · exact hs\\n have hscope' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping fieldName key value))\\n runtime.bindings :=\\n FunctionBody.scopeNamesPresent_of_included hscope hincl\\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\\n · let target := SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot keyNat)\\n set state' := { state with\\n transientStorage := fun o =>\\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMappingFieldSlots\\n fields fieldName runtime.world [slot] keyNat valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMapping fieldName key value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMappingFieldSlots, htrans, target]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, keyIR], valueIR])) =\\n .continue state' := by\\n have htargetMod :\\n Compiler.Proofs.solidityMappingSlot slot keyNat %\\n Compiler.Constants.evmModulus =\\n Compiler.Proofs.solidityMappingSlot slot keyNat := by\\n exact Nat.mod_eq_of_lt (by\\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat))\\n simp [execIRStmt, evalIRExpr, evalIRCall, evalIRExprs, hIRKey, hIRValue,\\n fieldStoreBuiltin, htrans, target, state', htargetMod,\\n Compiler.Proofs.abstractMappingSlot_eq_solidity,\\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMapping fieldName key value))\\n runtime'.bindings state' := by\\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping fieldName key value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\\n simp [stmtStepMatchesIRExec]\\n exact ⟨by\\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMappingFieldSlots,\\n htrans, target] using\\n (runtimeStateMatchesIR_writeTransientTarget\\n (target := target) hruntime hvalueLt),\\n hexact', hbounded, hscopeRuntime'⟩\\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\\n set state' := { state with\\n storage :=\\n Compiler.Proofs.abstractStoreMappingEntry\\n state.storage slot keyNat valueNat }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMappingSlots\\n runtime.world [slot] keyNat valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMapping fieldName key value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMappingFieldSlots, htransFalse]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, keyIR], valueIR])) =\\n .continue state' := by\\n simp [execIRStmt, evalIRExpr, hIRKey, hIRValue, fieldStoreBuiltin,\\n htransFalse, Compiler.Proofs.abstractStoreMappingEntry_eq, state']\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMapping fieldName key value))\\n runtime'.bindings state' :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (bindingsExactlyMatchIRVarsOnScope_writeMappingSlot hexact)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping fieldName key value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\\n simp [stmtStepMatchesIRExec]\\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMappingSlot\\n hruntime hresolvedNone hdynNone hvalueLt,\\n hexact', hbounded, hscopeRuntime'⟩\",\n \"n_chars\": 8061,\n \"n_subproofs\": 21,\n \"n_tactics\": 141,\n \"cyclomatic\": 7,\n \"n_automation\": 23,\n \"n_rewrites\": 3,\n \"n_structural\": 17,\n \"automation_only\": false,\n \"max_nesting\": 18\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingWord_singleSlot_of_slotSafety_preserves\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 165,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\\n have hkeySourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreKey hexact hinScopeKey hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\\n hruntime\\n have hvalueSourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hkeyIR] at hkeySourceEval\\n rw [hvalueIR] at hvalueSourceEval\\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\\n · simp [hIRKey, Option.bind] at hkeySourceEval\\n · simp [hIRKey, Option.bind] at hkeySourceEval\\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\\n hkeySourceEval.symm\\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\\n hvalueSourceEval.symm\\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\\n -- Get boundedness of valueNat\\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hValueSrc] at hvalueLt\\n simp at hvalueLt\\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\\n let writeSlotExpr :=\\n let mappingBase := YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, keyIR]\\n if wordOffset == 0 then mappingBase\\n else YulExpr.call \\\"add\\\" [mappingBase, YulExpr.lit wordOffset]\\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\\n simpa [writeSlotExpr, targetSlot] using\\n (evalIRExpr_mappingWordTarget_of_eval\\n (state := state) (slot := slot) (wordOffset := wordOffset) hIRKey)\\n -- Scope inclusion: stmtNextScope only adds expr names already in scope\\n have hTargetMod :\\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\\n Compiler.Constants.evmModulus = targetSlot := by\\n rw [show targetSlot =\\n (Verity.Core.Uint256.ofNat wordOffset +\\n Verity.Core.Uint256.ofNat\\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\\n simpa [Nat.add_comm] using\\n (uint256_add_val_eq_mod wordOffset\\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\\n have hincl : FunctionBody.scopeNamesIncluded\\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value)) scope := by\\n intro n hn\\n simp [stmtNextScope, collectStmtNames] at hn\\n rcases hn with hk | hv | hs\\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\\n · exact hs\\n have hscope' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\\n runtime.bindings :=\\n FunctionBody.scopeNamesPresent_of_included hscope hincl\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\\n · let target :=\\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\\n Compiler.Constants.evmModulus\\n set state' := { state with\\n transientStorage := fun o =>\\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMappingWordFieldSlots\\n fields fieldName runtime.world [slot] keyNat wordOffset valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMappingWord fieldName key wordOffset value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMappingWordFieldSlots,\\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [writeSlotExpr, valueIR])) = .continue state' := by\\n simpa [fieldStoreBuiltin, htrans, state', target, hTargetMod] using\\n (execIRStmt_tstore_of_eval\\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\\n hWriteSlotEval hIRValue)\\n have hIRExec : execIRStmts (1 + extraFuel + 1) state\\n [YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])] =\\n .continue state' := by\\n simp [execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\\n runtime'.bindings state' := by\\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, ?_, ?_⟩\\n · simpa [writeSlotExpr] using hIRExec\\n · simp [stmtStepMatchesIRExec]\\n exact ⟨by\\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMappingWordFieldSlots,\\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\\n (runtimeStateMatchesIR_writeTransientTarget\\n (target := target) hruntime hvalueLt),\\n hexact', hbounded, hscopeRuntime'⟩\\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\\n have htargetSlotNorm :\\n targetSlot % Compiler.Constants.evmModulus = targetSlot := by\\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\\n set state' := { state with\\n storage :=\\n Compiler.Proofs.abstractStoreStorageOrMapping\\n state.storage targetSlot valueNat }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMappingWordSlots\\n runtime.world [slot] keyNat wordOffset valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMappingWord fieldName key wordOffset value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMappingWordFieldSlots,\\n SourceSemantics.writeMappingTargets, SourceSemantics.writeAddressKeyedMappingWordSlots,\\n htransFalse, hTargetMod, htargetSlotNorm]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [writeSlotExpr, valueIR])) = .continue state' := by\\n simpa [fieldStoreBuiltin, htransFalse, state'] using\\n (execIRStmt_sstore_of_eval\\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\\n hWriteSlotEval hIRValue)\\n have hIRExec : execIRStmts (1 + extraFuel + 1) state\\n [YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName) [writeSlotExpr, valueIR])] =\\n .continue state' := by\\n simp [execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\\n runtime'.bindings state' :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMappingWord fieldName key wordOffset value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, ?_, ?_⟩\\n · simpa [writeSlotExpr] using hIRExec\\n · simp [stmtStepMatchesIRExec]\\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMappingWordSlot\\n hruntime hresolvedNone hdynNone hvalueLt,\\n hexact', hbounded, hscopeRuntime'⟩\",\n \"n_chars\": 9423,\n \"n_subproofs\": 22,\n \"n_tactics\": 165,\n \"cyclomatic\": 7,\n \"n_automation\": 26,\n \"n_rewrites\": 5,\n \"n_structural\": 17,\n \"automation_only\": false,\n \"max_nesting\": 18\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping2_singleSlot_of_slotSafety_preserves\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 172,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\\n let compiledIR := [YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\"\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, key1IR], key2IR], valueIR])]\\n -- Evaluate key1 expression\\n have hkey1SourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreKey1 hexact hinScopeKey1 hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey1)\\n hruntime\\n rw [hkey1IR] at hkey1SourceEval\\n simp [Except.toOption] at hkey1SourceEval\\n rcases hIRKey1 : evalIRExpr state key1IR with _ | key1Nat\\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\\n -- Evaluate key2 expression\\n have hkey2SourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreKey2 hexact hinScopeKey2 hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey2)\\n hruntime\\n rw [hkey2IR] at hkey2SourceEval\\n simp [Except.toOption] at hkey2SourceEval\\n rcases hIRKey2 : evalIRExpr state key2IR with _ | key2Nat\\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\\n -- Evaluate value expression\\n have hvalueSourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hvalueIR] at hvalueSourceEval\\n simp [Except.toOption] at hvalueSourceEval\\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n have hKey1Src : SourceSemantics.evalExpr fields runtime key1 = some key1Nat :=\\n hkey1SourceEval.symm\\n have hKey2Src : SourceSemantics.evalExpr fields runtime key2 = some key2Nat :=\\n hkey2SourceEval.symm\\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\\n hvalueSourceEval.symm\\n rcases hslotSafety runtime key1Nat key2Nat hKey1Src hKey2Src with ⟨hresolvedNone, hdynNone⟩\\n -- Get boundedness of valueNat\\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hValueSrc] at hvalueLt\\n simp at hvalueLt\\n -- Scope inclusion\\n have hincl : FunctionBody.scopeNamesIncluded\\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value)) scope := by\\n intro n hn\\n simp [stmtNextScope, collectStmtNames] at hn\\n rcases hn with hk1 | hk2 | hv | hs\\n · exact hinScopeKey1 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey1 n hk1)\\n · exact hinScopeKey2 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey2 n hk2)\\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\\n · exact hs\\n have hscope' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\\n runtime.bindings :=\\n FunctionBody.scopeNamesPresent_of_included hscope hincl\\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\\n · let target := SourceSemantics.wordNormalize\\n (Compiler.Proofs.abstractMappingSlot\\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\\n set state' := { state with\\n transientStorage := fun o =>\\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMapping2FieldSlots\\n fields fieldName runtime.world [slot] key1Nat key2Nat valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMapping2 fieldName key1 key2 value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMapping2FieldSlots, htrans, target]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\"\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, key1IR], key2IR], valueIR])) =\\n .continue state' := by\\n have htargetMod :\\n Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat %\\n Compiler.Constants.evmModulus =\\n Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat := by\\n exact Nat.mod_eq_of_lt (by\\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus\\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat))\\n simp [execIRStmt, evalIRExpr, evalIRCall, evalIRExprs, hIRKey1, hIRKey2, hIRValue,\\n fieldStoreBuiltin, htrans, target, state', htargetMod,\\n Compiler.Proofs.abstractMappingSlot_eq_solidity,\\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\\n runtime'.bindings state' := by\\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\\n simp [stmtStepMatchesIRExec]\\n exact ⟨by\\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2FieldSlots,\\n htrans, target] using\\n (runtimeStateMatchesIR_writeTransientTarget\\n (target := target) hruntime hvalueLt),\\n hexact', hbounded, hscopeRuntime'⟩\\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\\n set state' := { state with\\n storage :=\\n Compiler.Proofs.abstractStoreMappingEntry\\n state.storage\\n (Compiler.Proofs.abstractMappingSlot slot key1Nat)\\n key2Nat\\n valueNat }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMapping2Slots\\n runtime.world [slot] key1Nat key2Nat valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMapping2 fieldName key1 key2 value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMapping2FieldSlots, htransFalse]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [YulExpr.call \\\"mappingSlot\\\"\\n [YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, key1IR], key2IR], valueIR])) =\\n .continue state' := by\\n simp [execIRStmt, evalIRExpr, evalIRCall, evalIRExprs, hIRKey1, hIRKey2, hIRValue,\\n fieldStoreBuiltin, htransFalse,\\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean,\\n Compiler.Proofs.abstractStoreMappingEntry_eq, state']\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\\n runtime'.bindings state' :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (bindingsExactlyMatchIRVarsOnScope_writeMappingSlot hexact)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping2 fieldName key1 key2 value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\\n simp [stmtStepMatchesIRExec]\\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMapping2Slot\\n hruntime hresolvedNone hdynNone hvalueLt,\\n hexact', hbounded, hscopeRuntime'⟩\",\n \"n_chars\": 9940,\n \"n_subproofs\": 23,\n \"n_tactics\": 169,\n \"cyclomatic\": 8,\n \"n_automation\": 27,\n \"n_rewrites\": 4,\n \"n_structural\": 19,\n \"automation_only\": false,\n \"max_nesting\": 22\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 210,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\\n let compiledIR := [YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [let mappingBase := YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, key1IR]\\n let mappingSlot2 := YulExpr.call \\\"mappingSlot\\\" [mappingBase, key2IR]\\n if wordOffset == 0 then mappingSlot2\\n else YulExpr.call \\\"add\\\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])]\\n -- Evaluate key1 expression\\n have hkey1SourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreKey1 hexact hinScopeKey1 hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey1)\\n hruntime\\n rw [hkey1IR] at hkey1SourceEval\\n simp [Except.toOption] at hkey1SourceEval\\n rcases hIRKey1 : evalIRExpr state key1IR with _ | key1Nat\\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\\n -- Evaluate key2 expression\\n have hkey2SourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreKey2 hexact hinScopeKey2 hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey2)\\n hruntime\\n rw [hkey2IR] at hkey2SourceEval\\n simp [Except.toOption] at hkey2SourceEval\\n rcases hIRKey2 : evalIRExpr state key2IR with _ | key2Nat\\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\\n -- Evaluate value expression\\n have hvalueSourceEval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hvalueIR] at hvalueSourceEval\\n simp [Except.toOption] at hvalueSourceEval\\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n · simp [hIRValue, Option.bind] at hvalueSourceEval\\n have hKey1Src : SourceSemantics.evalExpr fields runtime key1 = some key1Nat :=\\n hkey1SourceEval.symm\\n have hKey2Src : SourceSemantics.evalExpr fields runtime key2 = some key2Nat :=\\n hkey2SourceEval.symm\\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\\n hvalueSourceEval.symm\\n rcases hslotSafety runtime key1Nat key2Nat hKey1Src hKey2Src with ⟨hresolvedNone, hdynNone⟩\\n -- Get boundedness of valueNat\\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\\n hcoreValue hexact hinScopeValue hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\\n hruntime\\n rw [hValueSrc] at hvalueLt\\n simp at hvalueLt\\n set targetSlot := mapping2WordTargetSlot slot key1Nat key2Nat wordOffset\\n let writeSlotExpr :=\\n let mappingBase := YulExpr.call \\\"mappingSlot\\\" [YulExpr.lit slot, key1IR]\\n let mappingSlot2 := YulExpr.call \\\"mappingSlot\\\" [mappingBase, key2IR]\\n if wordOffset == 0 then mappingSlot2\\n else YulExpr.call \\\"add\\\" [mappingSlot2, YulExpr.lit wordOffset]\\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\\n simpa [writeSlotExpr, targetSlot] using\\n (evalIRExpr_mapping2WordTarget_of_eval\\n (state := state) (slot := slot) (wordOffset := wordOffset) hIRKey1 hIRKey2)\\n have hTargetAdd :\\n targetSlot =\\n (Verity.Core.Uint256.ofNat wordOffset +\\n Verity.Core.Uint256.ofNat\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val := by\\n simpa [targetSlot] using\\n mapping2WordTargetSlot_eq_uint256_add slot key1Nat key2Nat wordOffset\\n have hTargetMod :\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\\n Compiler.Constants.evmModulus = targetSlot := by\\n rw [hTargetAdd]\\n simpa [Nat.add_comm] using\\n (uint256_add_val_eq_mod wordOffset\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).symm\\n -- Scope inclusion\\n have hincl : FunctionBody.scopeNamesIncluded\\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value)) scope := by\\n intro n hn\\n simp [stmtNextScope, collectStmtNames] at hn\\n rcases hn with hk1 | hk2 | hv | hs\\n · exact hinScopeKey1 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey1 n hk1)\\n · exact hinScopeKey2 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey2 n hk2)\\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\\n · exact hs\\n have hscope' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\\n runtime.bindings :=\\n FunctionBody.scopeNamesPresent_of_included hscope hincl\\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\\n · let target :=\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\\n Compiler.Constants.evmModulus\\n set state' := { state with\\n transientStorage := fun o =>\\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMapping2WordFieldSlots\\n fields fieldName runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [writeSlotExpr, valueIR])) = .continue state' := by\\n simpa [fieldStoreBuiltin, htrans, state', target, hTargetMod] using\\n (execIRStmt_tstore_of_eval\\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\\n hWriteSlotEval hIRValue)\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n change execIRStmts (1 + extraFuel + 1) state\\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [writeSlotExpr, valueIR])] = .continue state'\\n simp [execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\\n runtime'.bindings state' := by\\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\\n simp [stmtStepMatchesIRExec]\\n exact ⟨by\\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\\n (runtimeStateMatchesIR_writeTransientTarget\\n (target := target) hruntime hvalueLt),\\n hexact', hbounded, hscopeRuntime'⟩\\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\\n have htargetSlotNorm :\\n targetSlot % Compiler.Constants.evmModulus = targetSlot := by\\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\\n set state' := { state with\\n storage :=\\n Compiler.Proofs.abstractStoreStorageOrMapping\\n state.storage targetSlot valueNat }\\n set runtime' := { runtime with\\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\\n runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\\n SourceSemantics.writeMappingTargets, SourceSemantics.writeAddressKeyedMapping2WordSlots,\\n htransFalse, hTargetMod, htargetSlotNorm]\\n have hStoreEq :\\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot valueNat =\\n fun s =>\\n if s =\\n IRStorageSlot.ofNat\\n ((Verity.Core.Uint256.ofNat wordOffset +\\n Verity.Core.Uint256.ofNat\\n (Compiler.Proofs.solidityMappingSlot\\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) then\\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat valueNat\\n else\\n state.storage s := by\\n funext s\\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hTargetAdd]\\n have hExecStmt :\\n execIRStmt (extraFuel + 1) state\\n (YulStmt.exprStmt\\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [writeSlotExpr, valueIR])) = .continue state' := by\\n simpa [fieldStoreBuiltin, htransFalse, state'] using\\n (execIRStmt_sstore_of_eval\\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\\n hWriteSlotEval hIRValue)\\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue state' := by\\n change execIRStmts (1 + extraFuel + 1) state\\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\\n [writeSlotExpr, valueIR])] = .continue state'\\n simp [execIRStmts, hfuelEq, hExecStmt]\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\\n runtime'.bindings state' :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\\n hincl\\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\\n runtime'.bindings := by\\n simpa [runtime'] using hscope'\\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\\n simp [stmtStepMatchesIRExec]\\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\\n hruntime hresolvedNone hdynNone hvalueLt,\\n hexact', hbounded, hscopeRuntime'⟩\",\n \"n_chars\": 12280,\n \"n_subproofs\": 26,\n \"n_tactics\": 207,\n \"cyclomatic\": 8,\n \"n_automation\": 28,\n \"n_rewrites\": 8,\n \"n_structural\": 20,\n \"automation_only\": false,\n \"max_nesting\": 30\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"runtimeStateMatchesIR_writeTransientTarget","text":"private theorem runtimeStateMatchesIR_writeTransientTarget\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {target value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeTransientTargets runtime.world [target] value }\n { state with\n transientStorage := fun slot =>\n if slot = SourceSemantics.wordNormalize target then value else state.transientStorage slot } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, ?_, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr (by simp [SourceSemantics.writeTransientTargets])\n (by simp [SourceSemantics.writeTransientTargets])\n (by simp [SourceSemantics.writeTransientTargets]))\n · funext slot\n by_cases hslot : slot = SourceSemantics.wordNormalize target\n · subst hslot\n simp [SourceSemantics.writeTransientTargets]\n exact (Nat.mod_eq_of_lt (by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Verity.Core.Uint256.modulus] using hvalue)).symm\n · simp [SourceSemantics.writeTransientTargets, hslot]\n have hslot' : slot ≠ target % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hslot\n simp [hslot', congrFun htransient slot]\n\n","fan_in":6,"n_lines":35,"n_chars":1720,"n_subproofs":1,"n_tactics":21,"cyclomatic":2,"n_automation":8,"n_rewrites":2,"n_structural":6,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"runtimeStateMatchesIR_writeTransientTarget\",\n \"text\": \"private theorem runtimeStateMatchesIR_writeTransientTarget\\n {fields : List Field}\\n {runtime : SourceSemantics.RuntimeState}\\n {state : IRState}\\n {target value : Nat}\\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\\n (hvalue : value < Verity.Core.Uint256.modulus) :\\n FunctionBody.runtimeStateMatchesIR fields\\n { runtime with\\n world := SourceSemantics.writeTransientTargets runtime.world [target] value }\\n { state with\\n transientStorage := fun slot =>\\n if slot = SourceSemantics.wordNormalize target then value else state.transientStorage slot } := by\\n rcases hruntime with\\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\\n refine ⟨?_, ?_, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\\n · funext query\\n rw [hstorage]\\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\\n (SourceSemantics.encodeStorageAt_congr (by simp [SourceSemantics.writeTransientTargets])\\n (by simp [SourceSemantics.writeTransientTargets])\\n (by simp [SourceSemantics.writeTransientTargets]))\\n · funext slot\\n by_cases hslot : slot = SourceSemantics.wordNormalize target\\n · subst hslot\\n simp [SourceSemantics.writeTransientTargets]\\n exact (Nat.mod_eq_of_lt (by\\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\\n Verity.Core.Uint256.modulus] using hvalue)).symm\\n · simp [SourceSemantics.writeTransientTargets, hslot]\\n have hslot' : slot ≠ target % Compiler.Constants.evmModulus := by\\n simpa [SourceSemantics.wordNormalize] using hslot\\n simp [hslot', congrFun htransient slot]\\n\\n\",\n \"fan_in\": 6,\n \"n_lines\": 35,\n \"n_chars\": 1720,\n \"n_subproofs\": 1,\n \"n_tactics\": 21,\n \"cyclomatic\": 2,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 6,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_setStructMember2_singleSlot_of_slotSafety","fan_in":0,"n_deps_direct":3,"n_deps_transitive":31,"n_lines":48,"n_chars":3076,"n_subproofs":3,"n_tactics":14,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStep_setStructMember2_singleSlot_of_slotSafety\",\n \"fan_in\": 0,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 31,\n \"n_lines\": 48,\n \"n_chars\": 3076,\n \"n_subproofs\": 3,\n \"n_tactics\": 14,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":23,"string":"23"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\n simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\ntheorem mapping2WordTargetSlot_eq_uint256_add (slot key1 key2 wordOffset : Nat) :\n mapping2WordTargetSlot slot key1 key2 wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val := by\n unfold mapping2WordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\ntheorem findDynamicArrayElementAtSlotCopy_scanElements_wordNormalize\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy.scanElements\n (SourceSemantics.wordNormalize targetSlot) baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons _ rest ih =>\n simp only [findDynamicArrayElementAtSlotCopy.scanElements]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n\ntheorem findDynamicArrayElementAtSlotCopy_go_wordNormalize\n (remaining : List Field) (world : Verity.ContractState) (idx targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy.go world (SourceSemantics.wordNormalize targetSlot)\n remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [findDynamicArrayElementAtSlotCopy.go]\n rw [findDynamicArrayElementAtSlotCopy_scanElements_wordNormalize]\n split\n · split\n · rfl\n · exact ih (idx + 1)\n · exact ih (idx + 1)\n\ntheorem findDynamicArrayElementAtSlotCopy_wordNormalize\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy fields world (SourceSemantics.wordNormalize targetSlot) =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset query value : Nat}\n (hneq :\n query ≠ mapping2WordTargetSlot slot key1 key2 wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq :\n query =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mapping2WordTargetSlot slot key1 key2 wordOffset := by\n rw [mapping2WordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 %\n Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)\n wordOffset Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset value : Nat}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = value := by\n rw [encodeStorageAt_eq_copy]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = none := by\n rw [findResolvedFieldAtSlotCopy_wordNormalize]\n exact hresolved\n simp only [encodeStorageAtCopy, hresolved']\n have harray : (SourceSemantics.writeAddressKeyedMapping2WordSlots\n world [slot] key1 key2 wordOffset value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset))\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset))\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2]\n rw [findDynamicArrayElementAtSlotCopy_wordNormalize]\n exact hdyn\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, mapping2WordTargetSlot,\n SourceSemantics.wordNormalize, Verity.Core.Uint256.val_ofNat]\n have htargetLt :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).isLt\n simp [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n htargetLt, Nat.mod_eq_of_lt hvalue]\n simpa [Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using hvalue\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot key1 key2 wordOffset value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1 key2 wordOffset value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mapping2WordTargetSlot slot key1 key2 wordOffset)\n value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat (mapping2WordTargetSlot slot key1 key2 wordOffset)\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) =\n (runtime.world.storage (mapping2WordTargetSlot slot key1 key2 wordOffset)).val := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved, hdyn]\n simp only [hstorage, henc]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize,\n mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n SourceSemantics.wordNormalize_idem, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world)\n (slot := slot) (key1 := key1) (key2 := key2) (wordOffset := wordOffset)\n (value := value) hresolved hdyn hvalue).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key1 := key1)\n (key2 := key2) (wordOffset := wordOffset) (query := query.toNat) (value := value)\n (by simpa [mapping2WordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate theorem findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton\n {fields : List Field} {name : String} {slot : Nat}\n (h : findFieldWriteSlots fields name = some [slot]) :\n ∃ f, findFieldWithResolvedSlot fields name = some (f, slot) ∧ f.aliasSlots = [] := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWriteSlotsCopyFrom fields idx name = some [slot] →\n ∃ f, findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) ∧\n f.aliasSlots = [] by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWriteSlotsCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWriteSlotsCopyFrom at h\n unfold findFieldWithResolvedSlotCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hslot, halias⟩\n exact ⟨hd, by simpa [hslot, halias]⟩\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem evalIRExpr_mappingSlot2_of_eval\n {state : IRState} {slot key1Nat key2Nat : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [key1IR, key2IR])\n (keyVals := [key1Nat, key2Nat])\n (by simp [hkey1, hkey2] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [key1IR, key2IR] [key1Nat, key2Nat]))\n\nprivate theorem evalIRExpr_mappingSlot2_add_of_eval\n {state : IRState} {slot key1Nat key2Nat wordOffset : Nat}\n {key1IR key2IR : YulExpr}\n (hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)) :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR],\n YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) := by\n have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n (b := wordOffset)\n hMappingSlot2Eval\n (by simp [evalIRExpr])\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc,\n Nat.add_comm, Nat.add_left_comm] using hAddEval\n\nprivate theorem evalIRExpr_mapping2WordTarget_of_eval\n {state : IRState} {slot key1Nat key2Nat wordOffset : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIRExpr state\n (let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]) =\n some (mapping2WordTargetSlot slot key1Nat key2Nat wordOffset) := by\n have hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat) :=\n evalIRExpr_mappingSlot2_of_eval hkey1 hkey2\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat <\n Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n simpa [mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.mod_eq_of_lt hlt] using\n hMappingSlot2Eval\n · have hAddEval' :=\n evalIRExpr_mappingSlot2_add_of_eval\n (wordOffset := wordOffset)\n hMappingSlot2Eval\n simpa [hzero, mapping2WordTargetSlot_eq_uint256_add] using hAddEval'\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key1 key2 value : Expr}\n {wordOffset : Nat}\n {key1IR key2IR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey1 : FunctionBody.ExprCompileCore key1)\n (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2)\n (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] -\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime (.setMapping2Word fieldName key1 key2 wordOffset value) =\n sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])]\n -- Evaluate key1 expression\n have hkey1SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey1 hexact hinScopeKey1 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey1)\n hruntime\n rw [hkey1IR] at hkey1SourceEval\n simp [Except.toOption] at hkey1SourceEval\n rcases hIRKey1 : evalIRExpr state key1IR with _ | key1Nat\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n -- Evaluate key2 expression\n have hkey2SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey2 hexact hinScopeKey2 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey2)\n hruntime\n rw [hkey2IR] at hkey2SourceEval\n simp [Except.toOption] at hkey2SourceEval\n rcases hIRKey2 : evalIRExpr state key2IR with _ | key2Nat\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n -- Evaluate value expression\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKey1Src : SourceSemantics.evalExpr fields runtime key1 = some key1Nat :=\n hkey1SourceEval.symm\n have hKey2Src : SourceSemantics.evalExpr fields runtime key2 = some key2Nat :=\n hkey2SourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime key1Nat key2Nat hKey1Src hKey2Src with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set targetSlot := mapping2WordTargetSlot slot key1Nat key2Nat wordOffset\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n simpa [writeSlotExpr, targetSlot] using\n (evalIRExpr_mapping2WordTarget_of_eval\n (state := state) (slot := slot) (wordOffset := wordOffset) hIRKey1 hIRKey2)\n have hTargetAdd :\n targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val := by\n simpa [targetSlot] using\n mapping2WordTargetSlot_eq_uint256_add slot key1Nat key2Nat wordOffset\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [hTargetAdd]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).symm\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk1 | hk2 | hv | hs\n · exact hinScopeKey1 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey1 n hk1)\n · exact hinScopeKey2 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey2 n hk2)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target :=\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordFieldSlots\n fields fieldName runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htrans, state', target, hTargetMod] using\n (execIRStmt_tstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨by sorry,\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n have htargetSlotNorm :\n targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage targetSlot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, SourceSemantics.writeAddressKeyedMapping2WordSlots,\n htransFalse, hTargetMod, htargetSlotNorm]\n have hStoreEq :\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot valueNat =\n fun s =>\n if s =\n IRStorageSlot.ofNat\n ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat valueNat\n else\n state.storage s := by\n funext s\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hTargetAdd]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htransFalse, state'] using\n (execIRStmt_sstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩\n\nprivate theorem compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\n {fields : List Field} {scope : List String}\n {fieldName memberName : String} {key1 key2 value : Expr}\n {wordOffset : Nat} {members : List StructMember}\n {key1IR key2IR valueIR : YulExpr} {slot : Nat}\n (hcoreKey1 : FunctionBody.ExprCompileCore key1)\n (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2)\n (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hmembers : findStructMembers fields fieldName = some members)\n (hmember : findStructMember members memberName =\n some { name := memberName, wordOffset := wordOffset, packed := none })\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] -\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setStructMember2 fieldName key1 key2 memberName value) = sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setStructMember2 fieldName key1 key2 memberName value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n obtain ⟨sourceResult, irExec, hSrcMappingWord, hIRExec, hmatch⟩ :=\n compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\n runtime state extraFuel hexact hscope hbounded hruntime hslack\n refine ⟨sourceResult, irExec, ?_, hIRExec, ?_⟩\n · rw [← hSrcMappingWord]\n simp only [SourceSemantics.execStmt, hwriteSlots, hmembers]\n cases SourceSemantics.evalExpr fields runtime key1 <;>\n cases SourceSemantics.evalExpr fields runtime key2 <;>\n cases SourceSemantics.evalExpr fields runtime value <;>\n simp [hmember]\n · simpa [stmtStepMatchesIRExec, stmtNextScope, collectStmtNames]\n using hmatch\n\ntheorem compiledStmtStep_setStructMember2_singleSlot_of_slotSafety\n {fields : List Field} {scope : List String}\n {fieldName memberName : String} {key1 key2 value : Expr}\n {wordOffset : Nat} {members : List StructMember}\n {key1IR key2IR valueIR : YulExpr} {slot : Nat}\n (hmapping2 : isMapping2 fields fieldName = true)\n (hcoreKey1 : FunctionBody.ExprCompileCore key1) (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2) (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hmembers : findStructMembers fields fieldName = some members)\n (hmember : findStructMember members memberName =\n some { name := memberName, wordOffset := wordOffset, packed := none })\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStructMember2 fieldName key1 key2 memberName value)\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] where\n compileOk := by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember2,\n hmapping2, hmembers, hmember, hwriteSlots, hkey1IRInternal, hkey2IRInternal,\n hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hmembers hmember hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\n simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\ntheorem mapping2WordTargetSlot_eq_uint256_add (slot key1 key2 wordOffset : Nat) :\n mapping2WordTargetSlot slot key1 key2 wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val := by\n unfold mapping2WordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\ntheorem findDynamicArrayElementAtSlotCopy_scanElements_wordNormalize\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy.scanElements\n (SourceSemantics.wordNormalize targetSlot) baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons _ rest ih =>\n simp only [findDynamicArrayElementAtSlotCopy.scanElements]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n\ntheorem findDynamicArrayElementAtSlotCopy_go_wordNormalize\n (remaining : List Field) (world : Verity.ContractState) (idx targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy.go world (SourceSemantics.wordNormalize targetSlot)\n remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [findDynamicArrayElementAtSlotCopy.go]\n rw [findDynamicArrayElementAtSlotCopy_scanElements_wordNormalize]\n split\n · split\n · rfl\n · exact ih (idx + 1)\n · exact ih (idx + 1)\n\ntheorem findDynamicArrayElementAtSlotCopy_wordNormalize\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n findDynamicArrayElementAtSlotCopy fields world (SourceSemantics.wordNormalize targetSlot) =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset query value : Nat}\n (hneq :\n query ≠ mapping2WordTargetSlot slot key1 key2 wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq :\n query =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mapping2WordTargetSlot slot key1 key2 wordOffset := by\n rw [mapping2WordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 %\n Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2 + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)\n wordOffset Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n · simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset value : Nat}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = value := by\n rw [encodeStorageAt_eq_copy]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = none := by\n rw [findResolvedFieldAtSlotCopy_wordNormalize]\n exact hresolved\n simp only [encodeStorageAtCopy, hresolved']\n have harray : (SourceSemantics.writeAddressKeyedMapping2WordSlots\n world [slot] key1 key2 wordOffset value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMapping2WordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset)) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMapping2WordSlots world [slot] key1 key2 wordOffset value)\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset))\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (SourceSemantics.wordNormalize (mapping2WordTargetSlot slot key1 key2 wordOffset))\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2]\n rw [findDynamicArrayElementAtSlotCopy_wordNormalize]\n exact hdyn\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMapping2WordSlots, mapping2WordTargetSlot,\n SourceSemantics.wordNormalize, Verity.Core.Uint256.val_ofNat]\n have htargetLt :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1) key2)).isLt\n simp [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n htargetLt, Nat.mod_eq_of_lt hvalue]\n simpa [Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using hvalue\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeTransientTarget\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {target value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeTransientTargets runtime.world [target] value }\n { state with\n transientStorage := fun slot =>\n if slot = SourceSemantics.wordNormalize target then value else state.transientStorage slot } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, ?_, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr (by simp [SourceSemantics.writeTransientTargets])\n (by simp [SourceSemantics.writeTransientTargets])\n (by simp [SourceSemantics.writeTransientTargets]))\n · funext slot\n by_cases hslot : slot = SourceSemantics.wordNormalize target\n · subst hslot\n simp [SourceSemantics.writeTransientTargets]\n exact (Nat.mod_eq_of_lt (by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Verity.Core.Uint256.modulus] using hvalue)).symm\n · simp [SourceSemantics.writeTransientTargets, hslot]\n have hslot' : slot ≠ target % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hslot\n simp [hslot', congrFun htransient slot]\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot key1 key2 wordOffset value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) = none)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1 key2 wordOffset value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mapping2WordTargetSlot slot key1 key2 wordOffset)\n value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat (mapping2WordTargetSlot slot key1 key2 wordOffset)\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world\n (mapping2WordTargetSlot slot key1 key2 wordOffset) =\n (runtime.world.storage (mapping2WordTargetSlot slot key1 key2 wordOffset)).val := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved, hdyn]\n simp only [hstorage, henc]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize,\n mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n SourceSemantics.wordNormalize_idem, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world)\n (slot := slot) (key1 := key1) (key2 := key2) (wordOffset := wordOffset)\n (value := value) hresolved hdyn hvalue).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key1 := key1)\n (key2 := key2) (wordOffset := wordOffset) (query := query.toNat) (value := value)\n (by simpa [mapping2WordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate theorem findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton\n {fields : List Field} {name : String} {slot : Nat}\n (h : findFieldWriteSlots fields name = some [slot]) :\n ∃ f, findFieldWithResolvedSlot fields name = some (f, slot) ∧ f.aliasSlots = [] := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWriteSlotsCopyFrom fields idx name = some [slot] →\n ∃ f, findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) ∧\n f.aliasSlots = [] by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWriteSlotsCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWriteSlotsCopyFrom at h\n unfold findFieldWithResolvedSlotCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hslot, halias⟩\n exact ⟨hd, by simpa [hslot, halias]⟩\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem evalIRExpr_mappingSlot2_of_eval\n {state : IRState} {slot key1Nat key2Nat : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [key1IR, key2IR])\n (keyVals := [key1Nat, key2Nat])\n (by simp [hkey1, hkey2] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [key1IR, key2IR] [key1Nat, key2Nat]))\n\nprivate theorem evalIRExpr_mappingSlot2_add_of_eval\n {state : IRState} {slot key1Nat key2Nat wordOffset : Nat}\n {key1IR key2IR : YulExpr}\n (hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)) :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR],\n YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) := by\n have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n (b := wordOffset)\n hMappingSlot2Eval\n (by simp [evalIRExpr])\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc,\n Nat.add_comm, Nat.add_left_comm] using hAddEval\n\nprivate theorem evalIRExpr_mapping2WordTarget_of_eval\n {state : IRState} {slot key1Nat key2Nat wordOffset : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIRExpr state\n (let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]) =\n some (mapping2WordTargetSlot slot key1Nat key2Nat wordOffset) := by\n have hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR], key2IR]) =\n some (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat) :=\n evalIRExpr_mappingSlot2_of_eval hkey1 hkey2\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat <\n Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus\n (Compiler.Proofs.abstractMappingSlot slot key1Nat) key2Nat)\n simpa [mapping2WordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.mod_eq_of_lt hlt] using\n hMappingSlot2Eval\n · have hAddEval' :=\n evalIRExpr_mappingSlot2_add_of_eval\n (wordOffset := wordOffset)\n hMappingSlot2Eval\n simpa [hzero, mapping2WordTargetSlot_eq_uint256_add] using hAddEval'\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key1 key2 value : Expr}\n {wordOffset : Nat}\n {key1IR key2IR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey1 : FunctionBody.ExprCompileCore key1)\n (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2)\n (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] -\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime (.setMapping2Word fieldName key1 key2 wordOffset value) =\n sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR := [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])]\n -- Evaluate key1 expression\n have hkey1SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey1 hexact hinScopeKey1 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey1)\n hruntime\n rw [hkey1IR] at hkey1SourceEval\n simp [Except.toOption] at hkey1SourceEval\n rcases hIRKey1 : evalIRExpr state key1IR with _ | key1Nat\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n · simp [hIRKey1, Option.bind] at hkey1SourceEval\n -- Evaluate key2 expression\n have hkey2SourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey2 hexact hinScopeKey2 hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey2)\n hruntime\n rw [hkey2IR] at hkey2SourceEval\n simp [Except.toOption] at hkey2SourceEval\n rcases hIRKey2 : evalIRExpr state key2IR with _ | key2Nat\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n · simp [hIRKey2, Option.bind] at hkey2SourceEval\n -- Evaluate value expression\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKey1Src : SourceSemantics.evalExpr fields runtime key1 = some key1Nat :=\n hkey1SourceEval.symm\n have hKey2Src : SourceSemantics.evalExpr fields runtime key2 = some key2Nat :=\n hkey2SourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime key1Nat key2Nat hKey1Src hKey2Src with ⟨hresolvedNone, hdynNone⟩\n -- Get boundedness of valueNat\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set targetSlot := mapping2WordTargetSlot slot key1Nat key2Nat wordOffset\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset]\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n simpa [writeSlotExpr, targetSlot] using\n (evalIRExpr_mapping2WordTarget_of_eval\n (state := state) (slot := slot) (wordOffset := wordOffset) hIRKey1 hIRKey2)\n have hTargetAdd :\n targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val := by\n simpa [targetSlot] using\n mapping2WordTargetSlot_eq_uint256_add slot key1Nat key2Nat wordOffset\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [hTargetAdd]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).symm\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk1 | hk2 | hv | hs\n · exact hinScopeKey1 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey1 n hk1)\n · exact hinScopeKey2 n (collectExprNames_mem_exprBoundNames_of_core hcoreKey2 n hk2)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime.bindings :=\n FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · let target :=\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat + wordOffset) %\n Compiler.Constants.evmModulus\n set state' := { state with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize target then valueNat else state.transientStorage o }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordFieldSlots\n fields fieldName runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htrans, state', target, hTargetMod] using\n (execIRStmt_tstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' := by\n exact FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by intro name hname; simpa [IRState.getVar, state', runtime'] using hexact name hname)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨by\n simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\n (runtimeStateMatchesIR_writeTransientTarget\n (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n have htargetSlotNorm :\n targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage targetSlot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressKeyedMapping2WordSlots\n runtime.world [slot] key1Nat key2Nat wordOffset valueNat }\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMapping2Word fieldName key1 key2 wordOffset value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKey1Src, hKey2Src, hValueSrc, runtime',\n SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n SourceSemantics.writeMappingTargets, SourceSemantics.writeAddressKeyedMapping2WordSlots,\n htransFalse, hTargetMod, htargetSlotNorm]\n have hStoreEq :\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot valueNat =\n fun s =>\n if s =\n IRStorageSlot.ofNat\n ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot\n (Compiler.Proofs.solidityMappingSlot slot key1Nat) key2Nat)).val) then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat valueNat\n else\n state.storage s := by\n funext s\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hTargetAdd]\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])) = .continue state' := by\n simpa [fieldStoreBuiltin, htransFalse, state'] using\n (execIRStmt_sstore_of_eval\n (state := state) (slotExpr := writeSlotExpr) (valueExpr := valueIR)\n (slotVal := targetSlot) (valueVal := valueNat) (fuel := extraFuel)\n hWriteSlotEval hIRValue)\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n change execIRStmts (1 + extraFuel + 1) state\n [YulStmt.exprStmt (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr, valueIR])] = .continue state'\n simp [execIRStmts, hfuelEq, hExecStmt]\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot hexact)\n hincl\n have hscopeRuntime' : FunctionBody.scopeNamesPresent\n (stmtNextScope scope (.setMapping2Word fieldName key1 key2 wordOffset value))\n runtime'.bindings := by\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot\n hruntime hresolvedNone hdynNone hvalueLt,\n hexact', hbounded, hscopeRuntime'⟩\n\nprivate theorem compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\n {fields : List Field} {scope : List String}\n {fieldName memberName : String} {key1 key2 value : Expr}\n {wordOffset : Nat} {members : List StructMember}\n {key1IR key2IR valueIR : YulExpr} {slot : Nat}\n (hcoreKey1 : FunctionBody.ExprCompileCore key1)\n (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2)\n (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hmembers : findStructMembers fields fieldName = some members)\n (hmember : findStructMember members memberName =\n some { name := memberName, wordOffset := wordOffset, packed := none })\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] -\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setStructMember2 fieldName key1 key2 memberName value) = sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setStructMember2 fieldName key1 key2 memberName value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n obtain ⟨sourceResult, irExec, hSrcMappingWord, hIRExec, hmatch⟩ :=\n compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\n runtime state extraFuel hexact hscope hbounded hruntime hslack\n refine ⟨sourceResult, irExec, ?_, hIRExec, ?_⟩\n · rw [← hSrcMappingWord]\n simp only [SourceSemantics.execStmt, hwriteSlots, hmembers]\n cases SourceSemantics.evalExpr fields runtime key1 <;>\n cases SourceSemantics.evalExpr fields runtime key2 <;>\n cases SourceSemantics.evalExpr fields runtime value <;>\n simp [hmember]\n · simpa [stmtStepMatchesIRExec, stmtNextScope, collectStmtNames]\n using hmatch\n\ntheorem compiledStmtStep_setStructMember2_singleSlot_of_slotSafety\n {fields : List Field} {scope : List String}\n {fieldName memberName : String} {key1 key2 value : Expr}\n {wordOffset : Nat} {members : List StructMember}\n {key1IR key2IR valueIR : YulExpr} {slot : Nat}\n (hmapping2 : isMapping2 fields fieldName = true)\n (hcoreKey1 : FunctionBody.ExprCompileCore key1) (hinScopeKey1 : FunctionBody.exprBoundNamesInScope key1 scope)\n (hcoreKey2 : FunctionBody.ExprCompileCore key2) (hinScopeKey2 : FunctionBody.exprBoundNamesInScope key2 scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hmembers : findStructMembers fields fieldName = some members)\n (hmember : findStructMember members memberName =\n some { name := memberName, wordOffset := wordOffset, packed := none })\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat1 keyNat2,\n SourceSemantics.evalExpr fields runtime key1 = some keyNat1 →\n SourceSemantics.evalExpr fields runtime key2 = some keyNat2 →\n findResolvedFieldAtSlotCopy fields\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mapping2WordTargetSlot slot keyNat1 keyNat2 wordOffset) = none)\n (hkey1IR : CompilationModel.compileExpr fields .calldata key1 = Except.ok key1IR)\n (hkey2IR : CompilationModel.compileExpr fields .calldata key2 = Except.ok key2IR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStructMember2 fieldName key1 key2 memberName value)\n [YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, key1IR]\n let mappingSlot2 := YulExpr.call \"mappingSlot\" [mappingBase, key2IR]\n if wordOffset == 0 then mappingSlot2\n else YulExpr.call \"add\" [mappingSlot2, YulExpr.lit wordOffset], valueIR])] where\n compileOk := by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember2,\n hmapping2, hmembers, hmember, hwriteSlots, hkey1IRInternal, hkey2IRInternal,\n hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hmembers hmember hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -925,6 +925,40 @@\n rest\n value\n \n+private theorem runtimeStateMatchesIR_writeTransientTarget\n+ {fields : List Field}\n+ {runtime : SourceSemantics.RuntimeState}\n+ {state : IRState}\n+ {target value : Nat}\n+ (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n+ (hvalue : value < Verity.Core.Uint256.modulus) :\n+ FunctionBody.runtimeStateMatchesIR fields\n+ { runtime with\n+ world := SourceSemantics.writeTransientTargets runtime.world [target] value }\n+ { state with\n+ transientStorage := fun slot =>\n+ if slot = SourceSemantics.wordNormalize target then value else state.transientStorage slot } := by\n+ rcases hruntime with\n+ ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n+ refine ⟨?_, ?_, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n+ · funext query\n+ rw [hstorage]\n+ exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n+ (SourceSemantics.encodeStorageAt_congr (by simp [SourceSemantics.writeTransientTargets])\n+ (by simp [SourceSemantics.writeTransientTargets])\n+ (by simp [SourceSemantics.writeTransientTargets]))\n+ · funext slot\n+ by_cases hslot : slot = SourceSemantics.wordNormalize target\n+ · subst hslot\n+ simp [SourceSemantics.writeTransientTargets]\n+ exact (Nat.mod_eq_of_lt (by\n+ simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n+ Verity.Core.Uint256.modulus] using hvalue)).symm\n+ · simp [SourceSemantics.writeTransientTargets, hslot]\n+ have hslot' : slot ≠ target % Compiler.Constants.evmModulus := by\n+ simpa [SourceSemantics.wordNormalize] using hslot\n+ simp [hslot', congrFun htransient slot]\n+\n private theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n@@ -2468,7 +2502,11 @@\n simpa [runtime'] using hscope'\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n- exact ⟨by sorry,\n+ exact ⟨by\n+ simpa [runtime', state', SourceSemantics.writeAddressKeyedMapping2WordFieldSlots,\n+ SourceSemantics.writeMappingTargets, htrans, target, targetSlot, hTargetMod] using\n+ (runtimeStateMatchesIR_writeTransientTarget\n+ (target := target) hruntime hvalueLt),\n hexact', hbounded, hscopeRuntime'⟩\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21334,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_61"},"challenge_id":{"kind":"string","value":"4188872ddfe8f059"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":61,"string":"61"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_singleton","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n exact\n firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n hseen hfind hwrite (by simp) hunpacked","n_chars":121,"n_subproofs":0,"n_tactics":4,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"findResolvedFieldAtSlotCopyFrom_of_member","depth":1,"n_commands":0,"n_lines":66,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite","n_chars":3248,"n_subproofs":5,"n_tactics":66,"cyclomatic":6,"n_automation":17,"n_rewrites":11,"n_structural":15,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"theorem_name\": \"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_singleton\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n exact\\n firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\\n hseen hfind hwrite (by simp) hunpacked\",\n \"n_chars\": 121,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"findResolvedFieldAtSlotCopyFrom_of_member\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 66,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction fields generalizing seen idx with\\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\\n | cons field rest ih =>\\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\\n simp only [findResolvedFieldAtSlotCopyFrom]\\n by_cases hname : field.name == fieldName\\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\\n simp [hname] at hfind hwrite\\n obtain ⟨rfl, rfl⟩ := hfind\\n subst writeSlots\\n simp only [List.mem_cons] at hslot\\n rcases hslot with rfl | hmem\\n · simp\\n · rw [show\\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\\n (SourceSemantics.wordNormalize targetSlot) = true by\\n rw [List.contains_eq_mem]\\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\\n simp\\n · -- field.name doesn't match: recurse\\n simp [hname] at hfind hwrite\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\\n | none =>\\n rw [hc] at hnoConflict\\n -- After simp, condition is Prop-level: = or ∈\\n by_cases hcapture :\\n SourceSemantics.wordNormalize (field.slot.getD idx) =\\n SourceSemantics.wordNormalize targetSlot ∨\\n ∃ a ∈ field.aliasSlots,\\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\\n · exfalso\\n have htargetInEntries :\\n SourceSemantics.wordNormalize targetSlot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\\n · have hb := fieldWriteEntriesAt_base_mem idx field\\n rw [hbase] at hb\\n exact hb\\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\\n rw [haEq] at haIn\\n exact haIn\\n have htargetInSeen :\\n SourceSemantics.wordNormalize targetSlot ∈\\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\\n (fun entry => entry.1) := by\\n rw [List.map_append, List.mem_append, List.map_reverse]\\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\\n · push_neg at hcapture\\n rw [show\\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\\n SourceSemantics.wordNormalize targetSlot) ||\\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\\n (SourceSemantics.wordNormalize targetSlot)) = false by\\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\\n List.contains_eq_mem, List.mem_map]\\n exact ⟨hcapture.1, by\\n intro hmem\\n rcases hmem with ⟨a, haMem, haEq⟩\\n exact hcapture.2 a haMem haEq⟩]\\n exact ih hnoConflict hfind hwrite\",\n \"n_chars\": 3248,\n \"n_subproofs\": 5,\n \"n_tactics\": 66,\n \"cyclomatic\": 6,\n \"n_automation\": 17,\n \"n_rewrites\": 11,\n \"n_structural\": 15,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member","text":"private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\n","fan_in":2,"n_lines":63,"n_chars":2995,"n_subproofs":5,"n_tactics":41,"cyclomatic":5,"n_automation":11,"n_rewrites":3,"n_structural":12,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\",\n \"text\": \"private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\\n {seen : List (Nat × String × Option PackedBits)}\\n {fields : List Field}\\n {idx : Nat}\\n {fieldName : String}\\n {f : Field}\\n {slot : Nat}\\n {writeSlots : List Nat}\\n {targetSlot : Nat}\\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\\n (hfind :\\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\\n (hwrite :\\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\\n (hslot : targetSlot ∈ writeSlots)\\n (hunpacked : f.packedBits = none) :\\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\\n induction fields generalizing seen idx with\\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\\n | cons field rest ih =>\\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\\n simp only [firstFieldWriteSlotConflictCopyFrom]\\n by_cases hname : field.name == fieldName\\n · -- field.name matches: hfind and hwrite resolve here\\n simp [hname] at hfind hwrite\\n obtain ⟨rfl, rfl⟩ := hfind\\n subst hwrite\\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\\n -- and all packed bits = field.packedBits = none\\n have htarget_in_entries :\\n SourceSemantics.wordNormalize targetSlot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n simp only [List.mem_cons] at hslot\\n rcases hslot with hslot | halias\\n · subst targetSlot\\n exact fieldWriteEntriesAt_base_mem idx field\\n · exact fieldWriteEntriesAt_alias_mem halias\\n have hunpacked_entries :\\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\\n packed = none := by\\n intro packed hmem\\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\\n hseen htarget_in_entries hunpacked_entries\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | none => exact absurd hc hconflict\\n | some _ => simp\\n · -- field.name doesn't match: recurse\\n simp [hname] at hfind hwrite\\n have hseen' :\\n SourceSemantics.wordNormalize targetSlot ∈\\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\\n (fun entry => entry.1) := by\\n rw [List.map_append, List.mem_append]\\n exact Or.inr hseen\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | some _ => simp\\n | none => exact ih hseen' hfind hwrite\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 63,\n \"n_chars\": 2995,\n \"n_subproofs\": 5,\n \"n_tactics\": 41,\n \"cyclomatic\": 5,\n \"n_automation\": 11,\n \"n_rewrites\": 3,\n \"n_structural\": 12,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_setStorage_aliasSlots","fan_in":1,"n_deps_direct":6,"n_deps_transitive":30,"n_lines":178,"n_chars":8970,"n_subproofs":26,"n_tactics":142,"cyclomatic":5,"n_automation":22,"n_rewrites":4,"n_structural":13,"automation_only":false,"max_nesting":22}],"string":"[\n {\n \"name\": \"compiledStmtStep_setStorage_aliasSlots\",\n \"fan_in\": 1,\n \"n_deps_direct\": 6,\n \"n_deps_transitive\": 30,\n \"n_lines\": 178,\n \"n_chars\": 8970,\n \"n_subproofs\": 26,\n \"n_tactics\": 142,\n \"cyclomatic\": 5,\n \"n_automation\": 22,\n \"n_rewrites\": 4,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 22\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":25,"string":"25"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · sorry\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -467,6 +467,68 @@\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n \n+private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n+ {seen : List (Nat × String × Option PackedBits)}\n+ {fields : List Field}\n+ {idx : Nat}\n+ {fieldName : String}\n+ {f : Field}\n+ {slot : Nat}\n+ {writeSlots : List Nat}\n+ {targetSlot : Nat}\n+ (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n+ (hfind :\n+ findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n+ (hwrite :\n+ findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n+ (hslot : targetSlot ∈ writeSlots)\n+ (hunpacked : f.packedBits = none) :\n+ firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n+ induction fields generalizing seen idx with\n+ | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n+ | cons field rest ih =>\n+ simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n+ simp only [findFieldWriteSlotsCopyFrom] at hwrite\n+ simp only [firstFieldWriteSlotConflictCopyFrom]\n+ by_cases hname : field.name == fieldName\n+ · -- field.name matches: hfind and hwrite resolve here\n+ simp [hname] at hfind hwrite\n+ obtain ⟨rfl, rfl⟩ := hfind\n+ subst hwrite\n+ -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n+ -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n+ -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n+ -- and all packed bits = field.packedBits = none\n+ have htarget_in_entries :\n+ SourceSemantics.wordNormalize targetSlot ∈\n+ (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n+ simp only [List.mem_cons] at hslot\n+ rcases hslot with hslot | halias\n+ · subst targetSlot\n+ exact fieldWriteEntriesAt_base_mem idx field\n+ · exact fieldWriteEntriesAt_alias_mem halias\n+ have hunpacked_entries :\n+ ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n+ packed = none := by\n+ intro packed hmem\n+ exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n+ have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n+ hseen htarget_in_entries hunpacked_entries\n+ cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n+ | none => exact absurd hc hconflict\n+ | some _ => simp\n+ · -- field.name doesn't match: recurse\n+ simp [hname] at hfind hwrite\n+ have hseen' :\n+ SourceSemantics.wordNormalize targetSlot ∈\n+ ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n+ (fun entry => entry.1) := by\n+ rw [List.map_append, List.mem_append]\n+ exact Or.inr hseen\n+ cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n+ | some _ => simp\n+ | none => exact ih hseen' hfind hwrite\n+\n theorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n@@ -515,7 +577,25 @@\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n- · sorry\n+ · exfalso\n+ have htargetInEntries :\n+ SourceSemantics.wordNormalize targetSlot ∈\n+ (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n+ rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n+ · have hb := fieldWriteEntriesAt_base_mem idx field\n+ rw [hbase] at hb\n+ exact hb\n+ · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n+ rw [haEq] at haIn\n+ exact haIn\n+ have htargetInSeen :\n+ SourceSemantics.wordNormalize targetSlot ∈\n+ ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n+ (fun entry => entry.1) := by\n+ rw [List.map_append, List.mem_append, List.map_reverse]\n+ exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n+ exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n+ htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21335,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_62"},"challenge_id":{"kind":"string","value":"5af480282371e01e"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":62,"string":"62"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked","n_chars":130,"n_subproofs":0,"n_tactics":4,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setStorage_aliasSlots","depth":1,"n_commands":0,"n_lines":148,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩","n_chars":7556,"n_subproofs":26,"n_tactics":142,"cyclomatic":5,"n_automation":22,"n_rewrites":4,"n_structural":13,"automation_only":false,"max_nesting":22}],"string":"[\n {\n \"theorem_name\": \"findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n exact\\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\\n hnoConflict hfind hwrite (by simp) hunpacked\",\n \"n_chars\": 130,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setStorage_aliasSlots\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 148,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n cases hty : f.ty with\\n | adt name maxFields =>\\n exact False.elim (hNotAdt name maxFields hty)\\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\\n pure, Except.pure, Bind.bind, Except.bind]\\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\\n let slots := slot :: f.aliasSlots\\n let blockBody :=\\n [YulStmt.let_ \\\"__compat_value\\\" valueIR] ++\\n slots.map (fun writeSlot =>\\n YulStmt.exprStmt\\n (YulExpr.call \\\"sstore\\\" [YulExpr.lit writeSlot, YulExpr.ident \\\"__compat_value\\\"]))\\n let compiledIR := [YulStmt.block blockBody]\\n have heval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcore hexact hinScope hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\\n hruntime\\n rw [hvalueIR] at heval\\n simp [Except.toOption] at heval\\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\\n · simp [hIRValue, Option.bind] at heval\\n · simp [hIRValue, Option.bind] at heval\\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\\n heval.symm\\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\\n -- Prove sizeOf of any YulStmt list ≥ length + 1\\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\\n intro l\\n induction l with\\n | nil => simp\\n | cons h t ih =>\\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\\n omega\\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\\n simpa [compiledIR] using hslack\\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\\n -- blockBody.length = 1 + slots.length (let_ + map)\\n have hBodyLen : blockBody.length = 1 + slots.length := by\\n simp [blockBody, slots]; omega\\n have hBodyBound := hSizeOfListBound blockBody\\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\\n dsimp only [compiledIR]; rfl\\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\\n simp [YulStmt.block.sizeOf_spec]\\n omega\\n let bodyExtraFuel := extraFuel - (slots.length + 2)\\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\\n dsimp [bodyExtraFuel]\\n omega\\n have hresolvedSlots :\\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\\n intro writeSlot hmem\\n exact\\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\\n hnoConflict hfind hwriteSlots hmem hunpacked\\n have hbody :\\n execIRStmts extraFuel state blockBody =\\n .continue\\n { state.setVar \\\"__compat_value\\\" valueNat with\\n storage :=\\n abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage\\n slots\\n valueNat } := by\\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\\n bodyExtraFuel state slots \\\"__compat_value\\\" valueIR valueNat hvalueEval\\n rw [hbodyFuelEq] at this\\n simpa [blockBody, slots] using this\\n have hwhole :\\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue\\n { state.setVar \\\"__compat_value\\\" valueNat with\\n storage :=\\n abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage\\n slots\\n valueNat } := by\\n have hblock := execIRStmts_single_block_of_continue\\n extraFuel state\\n { state.setVar \\\"__compat_value\\\" valueNat with\\n storage :=\\n abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage\\n slots\\n valueNat }\\n blockBody\\n hbody\\n convert hblock using 2\\n simp [compiledIR]; omega\\n -- Prove value bound\\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\\n hcore hexact hinScope hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\\n hruntime\\n rw [hValueSrc] at hvalueLt\\n simp at hvalueLt\\n -- Source execution\\n have hfieldTransient :\\n SourceSemantics.fieldIsTransient fields fieldName = false := by\\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setStorage fieldName value) = .continue\\n { runtime with\\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\\n -- Scope inclusion\\n have hincl : FunctionBody.scopeNamesIncluded\\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\\n intro n hn\\n simp [stmtNextScope, collectStmtNames] at hn\\n rcases hn with hv | hs\\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\\n · exact hs\\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\\n -- Runtime state match\\n have hruntimeSet :\\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \\\"__compat_value\\\" valueNat) :=\\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\\n { (state.setVar \\\"__compat_value\\\" valueNat) with\\n storage := abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage slots valueNat } :=\\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\\n -- Bindings match\\n have hexactSet :\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\\n (state.setVar \\\"__compat_value\\\" valueNat) :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\\n { (state.setVar \\\"__compat_value\\\" valueNat) with\\n storage := abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage slots valueNat } :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\\n simp [stmtStepMatchesIRExec, slots]\\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\",\n \"n_chars\": 7556,\n \"n_subproofs\": 26,\n \"n_tactics\": 142,\n \"cyclomatic\": 5,\n \"n_automation\": 22,\n \"n_rewrites\": 4,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 22\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member","text":"theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\n","fan_in":2,"n_lines":27,"n_chars":1296,"n_subproofs":3,"n_tactics":11,"cyclomatic":1,"n_automation":0,"n_rewrites":2,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\",\n \"text\": \"theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\\n {fields : List Field}\\n {fieldName : String}\\n {f : Field}\\n {slot : Nat}\\n {writeSlots : List Nat}\\n {targetSlot : Nat}\\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\\n (hslot : targetSlot ∈ writeSlots)\\n (hunpacked : f.packedBits = none) :\\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\\n -- Bridge result\\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\\n -- Bridge hypotheses\\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\\n exact findResolvedFieldAtSlotCopyFrom_of_member\\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 27,\n \"n_chars\": 1296,\n \"n_subproofs\": 3,\n \"n_tactics\": 11,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 2,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_setStorage_of_validateIdentifierShapes","fan_in":1,"n_deps_direct":3,"n_deps_transitive":41,"n_lines":73,"n_chars":2940,"n_subproofs":0,"n_tactics":41,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":4,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"compiledStmtStep_setStorage_of_validateIdentifierShapes\",\n \"fan_in\": 1,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 41,\n \"n_lines\": 73,\n \"n_chars\": 2940,\n \"n_subproofs\": 0,\n \"n_tactics\": 41,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":35,"string":"35"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := sorry\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem compatScratch_startsWith_reserved\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__\" = true := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n\nprivate theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__immutable_\" = false := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n\nprivate theorem validateIdentifierShapes_fieldName_ne_reservedScratch\n {spec : CompilationModel}\n {name : String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hmem : name ∈ spec.fields.map (·.name)) :\n name ≠ \"__compat_value\" ∧\n name ≠ \"__compat_packed\" ∧\n name ≠ \"__compat_slot_word\" ∧\n name ≠ \"__compat_slot_cleared\" := by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n CompilationModel.validateIdentifierShapes_field_avoidReservedCompilerPrefix hvalidate hfield\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_value\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inl rfl)\n have himm : \"__compat_value\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_packed\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inl rfl)\n have himm : \"__compat_packed\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_word\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inl rfl)\n have himm : \"__compat_slot_word\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_cleared\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inr rfl)\n have himm : \"__compat_slot_cleared\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inr rfl)\n simpa [hEq, hprefix, himm])\n\nprivate theorem scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name))) :\n scopeAvoidsReservedCompilerPrefix scope := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hmem\n have hname := hscopeNames \"__compat_value\" hmem\n have hname' :\n \"__compat_value\" ∈ fn.params.map (·.name) ∨\n \"__compat_value\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_value\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_value\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inl rfl))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_packed\" hmem\n have hname' :\n \"__compat_packed\" ∈ fn.params.map (·.name) ∨\n \"__compat_packed\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_packed\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_packed\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_word\" hmem\n have hname' :\n \"__compat_slot_word\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_word\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_word\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_word\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_cleared\" hmem\n have hname' :\n \"__compat_slot_cleared\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_cleared\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_cleared\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_cleared\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.2 rfl\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := sorry\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name)))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR, CompiledStmtStep spec.fields scope (.setStorage fieldName value) compiledIR := by\n by_cases halias : f.aliasSlots = []\n · refine ⟨[YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])], ?_⟩\n apply compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := ?_)\n (halias := halias)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n simpa [halias] using hwriteSlots\n · refine\n ⟨[YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))],\n ?_⟩\n apply compiledStmtStep_setStorage_aliasSlots\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (halias := halias)\n (hscopeReserved := scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n hvalidate hfn hscopeNames)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem compatScratch_startsWith_reserved\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__\" = true := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n\nprivate theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__immutable_\" = false := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n\nprivate theorem validateIdentifierShapes_fieldName_ne_reservedScratch\n {spec : CompilationModel}\n {name : String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hmem : name ∈ spec.fields.map (·.name)) :\n name ≠ \"__compat_value\" ∧\n name ≠ \"__compat_packed\" ∧\n name ≠ \"__compat_slot_word\" ∧\n name ≠ \"__compat_slot_cleared\" := by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n CompilationModel.validateIdentifierShapes_field_avoidReservedCompilerPrefix hvalidate hfield\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_value\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inl rfl)\n have himm : \"__compat_value\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_packed\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inl rfl)\n have himm : \"__compat_packed\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_word\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inl rfl)\n have himm : \"__compat_slot_word\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_cleared\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inr rfl)\n have himm : \"__compat_slot_cleared\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inr rfl)\n simpa [hEq, hprefix, himm])\n\nprivate theorem scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name))) :\n scopeAvoidsReservedCompilerPrefix scope := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hmem\n have hname := hscopeNames \"__compat_value\" hmem\n have hname' :\n \"__compat_value\" ∈ fn.params.map (·.name) ∨\n \"__compat_value\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_value\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_value\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inl rfl))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_packed\" hmem\n have hname' :\n \"__compat_packed\" ∈ fn.params.map (·.name) ∨\n \"__compat_packed\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_packed\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_packed\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_word\" hmem\n have hname' :\n \"__compat_slot_word\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_word\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_word\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_word\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_cleared\" hmem\n have hname' :\n \"__compat_slot_cleared\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_cleared\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_cleared\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_cleared\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.2 rfl\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name)))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR, CompiledStmtStep spec.fields scope (.setStorage fieldName value) compiledIR := by\n by_cases halias : f.aliasSlots = []\n · refine ⟨[YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])], ?_⟩\n apply compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := ?_)\n (halias := halias)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n simpa [halias] using hwriteSlots\n · refine\n ⟨[YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))],\n ?_⟩\n apply compiledStmtStep_setStorage_aliasSlots\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (halias := halias)\n (hscopeReserved := scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n hvalidate hfn hscopeNames)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -674,6 +674,32 @@\n | some _ =>\n simp [hc]\n \n+theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n+ {fields : List Field}\n+ {fieldName : String}\n+ {f : Field}\n+ {slot : Nat}\n+ {writeSlots : List Nat}\n+ {targetSlot : Nat}\n+ (hnoConflict : firstFieldWriteSlotConflict fields = none)\n+ (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n+ (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n+ (hslot : targetSlot ∈ writeSlots)\n+ (hunpacked : f.packedBits = none) :\n+ findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n+ -- Bridge result\n+ show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n+ rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n+ -- Bridge hypotheses\n+ have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n+ findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n+ have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n+ findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n+ have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n+ firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n+ exact findResolvedFieldAtSlotCopyFrom_of_member\n+ hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n+\n theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n@@ -683,7 +709,10 @@\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n- findResolvedFieldAtSlotCopy fields slot = some f := sorry\n+ findResolvedFieldAtSlotCopy fields slot = some f := by\n+ exact\n+ findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n+ hnoConflict hfind hwrite (by simp) hunpacked\n \n private theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n@@ -2690,7 +2719,11 @@\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n- ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := sorry\n+ ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n+ intro writeSlot hmem\n+ exact\n+ findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n+ hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21336,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_63"},"challenge_id":{"kind":"string","value":"92c9808cab04b41c"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":63,"string":"63"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked","n_chars":130,"n_subproofs":0,"n_tactics":4,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setStorage_aliasSlots","depth":1,"n_commands":0,"n_lines":148,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩","n_chars":7556,"n_subproofs":26,"n_tactics":142,"cyclomatic":5,"n_automation":22,"n_rewrites":4,"n_structural":13,"automation_only":false,"max_nesting":22}],"string":"[\n {\n \"theorem_name\": \"findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n exact\\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\\n hnoConflict hfind hwrite (by simp) hunpacked\",\n \"n_chars\": 130,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setStorage_aliasSlots\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 148,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n cases hty : f.ty with\\n | adt name maxFields =>\\n exact False.elim (hNotAdt name maxFields hty)\\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\\n pure, Except.pure, Bind.bind, Except.bind]\\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\\n let slots := slot :: f.aliasSlots\\n let blockBody :=\\n [YulStmt.let_ \\\"__compat_value\\\" valueIR] ++\\n slots.map (fun writeSlot =>\\n YulStmt.exprStmt\\n (YulExpr.call \\\"sstore\\\" [YulExpr.lit writeSlot, YulExpr.ident \\\"__compat_value\\\"]))\\n let compiledIR := [YulStmt.block blockBody]\\n have heval :=\\n FunctionBody.eval_compileExpr_core_of_scope\\n hcore hexact hinScope hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\\n hruntime\\n rw [hvalueIR] at heval\\n simp [Except.toOption] at heval\\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\\n · simp [hIRValue, Option.bind] at heval\\n · simp [hIRValue, Option.bind] at heval\\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\\n heval.symm\\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\\n -- Prove sizeOf of any YulStmt list ≥ length + 1\\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\\n intro l\\n induction l with\\n | nil => simp\\n | cons h t ih =>\\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\\n omega\\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\\n simpa [compiledIR] using hslack\\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\\n -- blockBody.length = 1 + slots.length (let_ + map)\\n have hBodyLen : blockBody.length = 1 + slots.length := by\\n simp [blockBody, slots]; omega\\n have hBodyBound := hSizeOfListBound blockBody\\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\\n dsimp only [compiledIR]; rfl\\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\\n simp [YulStmt.block.sizeOf_spec]\\n omega\\n let bodyExtraFuel := extraFuel - (slots.length + 2)\\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\\n dsimp [bodyExtraFuel]\\n omega\\n have hresolvedSlots :\\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\\n intro writeSlot hmem\\n exact\\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\\n hnoConflict hfind hwriteSlots hmem hunpacked\\n have hbody :\\n execIRStmts extraFuel state blockBody =\\n .continue\\n { state.setVar \\\"__compat_value\\\" valueNat with\\n storage :=\\n abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage\\n slots\\n valueNat } := by\\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\\n bodyExtraFuel state slots \\\"__compat_value\\\" valueIR valueNat hvalueEval\\n rw [hbodyFuelEq] at this\\n simpa [blockBody, slots] using this\\n have hwhole :\\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\\n .continue\\n { state.setVar \\\"__compat_value\\\" valueNat with\\n storage :=\\n abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage\\n slots\\n valueNat } := by\\n have hblock := execIRStmts_single_block_of_continue\\n extraFuel state\\n { state.setVar \\\"__compat_value\\\" valueNat with\\n storage :=\\n abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage\\n slots\\n valueNat }\\n blockBody\\n hbody\\n convert hblock using 2\\n simp [compiledIR]; omega\\n -- Prove value bound\\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\\n hcore hexact hinScope hbounded\\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\\n hruntime\\n rw [hValueSrc] at hvalueLt\\n simp at hvalueLt\\n -- Source execution\\n have hfieldTransient :\\n SourceSemantics.fieldIsTransient fields fieldName = false := by\\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\\n have hSrcExec : SourceSemantics.execStmt fields runtime\\n (.setStorage fieldName value) = .continue\\n { runtime with\\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\\n -- Scope inclusion\\n have hincl : FunctionBody.scopeNamesIncluded\\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\\n intro n hn\\n simp [stmtNextScope, collectStmtNames] at hn\\n rcases hn with hv | hs\\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\\n · exact hs\\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\\n -- Runtime state match\\n have hruntimeSet :\\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \\\"__compat_value\\\" valueNat) :=\\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\\n { (state.setVar \\\"__compat_value\\\" valueNat) with\\n storage := abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage slots valueNat } :=\\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\\n -- Bindings match\\n have hexactSet :\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\\n (state.setVar \\\"__compat_value\\\" valueNat) :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\\n { (state.setVar \\\"__compat_value\\\" valueNat) with\\n storage := abstractStoreStorageOrMappingMany\\n (state.setVar \\\"__compat_value\\\" valueNat).storage slots valueNat } :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\\n simp [stmtStepMatchesIRExec, slots]\\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\",\n \"n_chars\": 7556,\n \"n_subproofs\": 26,\n \"n_tactics\": 142,\n \"cyclomatic\": 5,\n \"n_automation\": 22,\n \"n_rewrites\": 4,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 22\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member","text":"theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\n","fan_in":2,"n_lines":27,"n_chars":1296,"n_subproofs":3,"n_tactics":11,"cyclomatic":1,"n_automation":0,"n_rewrites":2,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\",\n \"text\": \"theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\\n {fields : List Field}\\n {fieldName : String}\\n {f : Field}\\n {slot : Nat}\\n {writeSlots : List Nat}\\n {targetSlot : Nat}\\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\\n (hslot : targetSlot ∈ writeSlots)\\n (hunpacked : f.packedBits = none) :\\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\\n -- Bridge result\\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\\n -- Bridge hypotheses\\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\\n exact findResolvedFieldAtSlotCopyFrom_of_member\\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 27,\n \"n_chars\": 1296,\n \"n_subproofs\": 3,\n \"n_tactics\": 11,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 2,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline","fan_in":1,"n_deps_direct":1,"n_deps_transitive":42,"n_lines":88,"n_chars":3627,"n_subproofs":3,"n_tactics":52,"cyclomatic":6,"n_automation":5,"n_rewrites":2,"n_structural":19,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\",\n \"fan_in\": 1,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 42,\n \"n_lines\": 88,\n \"n_chars\": 3627,\n \"n_subproofs\": 3,\n \"n_tactics\": 52,\n \"cyclomatic\": 6,\n \"n_automation\": 5,\n \"n_rewrites\": 2,\n \"n_structural\": 19,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":36,"string":"36"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := sorry\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem compatScratch_startsWith_reserved\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__\" = true := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n\nprivate theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__immutable_\" = false := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n\nprivate theorem validateIdentifierShapes_fieldName_ne_reservedScratch\n {spec : CompilationModel}\n {name : String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hmem : name ∈ spec.fields.map (·.name)) :\n name ≠ \"__compat_value\" ∧\n name ≠ \"__compat_packed\" ∧\n name ≠ \"__compat_slot_word\" ∧\n name ≠ \"__compat_slot_cleared\" := by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n CompilationModel.validateIdentifierShapes_field_avoidReservedCompilerPrefix hvalidate hfield\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_value\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inl rfl)\n have himm : \"__compat_value\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_packed\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inl rfl)\n have himm : \"__compat_packed\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_word\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inl rfl)\n have himm : \"__compat_slot_word\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_cleared\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inr rfl)\n have himm : \"__compat_slot_cleared\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inr rfl)\n simpa [hEq, hprefix, himm])\n\nprivate theorem scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name))) :\n scopeAvoidsReservedCompilerPrefix scope := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hmem\n have hname := hscopeNames \"__compat_value\" hmem\n have hname' :\n \"__compat_value\" ∈ fn.params.map (·.name) ∨\n \"__compat_value\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_value\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_value\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inl rfl))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_packed\" hmem\n have hname' :\n \"__compat_packed\" ∈ fn.params.map (·.name) ∨\n \"__compat_packed\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_packed\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_packed\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_word\" hmem\n have hname' :\n \"__compat_slot_word\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_word\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_word\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_word\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_cleared\" hmem\n have hname' :\n \"__compat_slot_cleared\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_cleared\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_cleared\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_cleared\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.2 rfl\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := sorry\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name)))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR, CompiledStmtStep spec.fields scope (.setStorage fieldName value) compiledIR := by\n by_cases halias : f.aliasSlots = []\n · refine ⟨[YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])], ?_⟩\n apply compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := ?_)\n (halias := halias)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n simpa [halias] using hwriteSlots\n · refine\n ⟨[YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))],\n ?_⟩\n apply compiledStmtStep_setStorage_aliasSlots\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (halias := halias)\n (hscopeReserved := scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n hvalidate hfn hscopeNames)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hprefix :\n StmtListScopeDiscipline\n (spec.fields.map (·.name))\n (fn.params.map (·.name))\n «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes\n (scope := List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (hvalidate := hvalidate)\n (hfn := hfn)\n (hscopeNames := ?_)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n intro name hmem\n have hscopeNames := stmtListScopeDiscipline_scope_names hprefix name hmem\n have collectStmtListBindNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListBindNames a →\n x ∈ collectStmtListBindNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListBindNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListBindNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n have collectStmtListAssignedNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListAssignedNames a →\n x ∈ collectStmtListAssignedNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListAssignedNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListAssignedNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n simp only [List.mem_append] at hscopeNames ⊢\n rcases hscopeNames with ((h | h) | h) | h\n · exact Or.inl (Or.inl (Or.inl h))\n · exact Or.inl (Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListBindNames_prefix_subset _ _ _ h)))\n · exact Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListAssignedNames_prefix_subset _ _ _ h))\n · exact Or.inr h\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem compatScratch_startsWith_reserved\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__\" = true := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n\nprivate theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__immutable_\" = false := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n\nprivate theorem validateIdentifierShapes_fieldName_ne_reservedScratch\n {spec : CompilationModel}\n {name : String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hmem : name ∈ spec.fields.map (·.name)) :\n name ≠ \"__compat_value\" ∧\n name ≠ \"__compat_packed\" ∧\n name ≠ \"__compat_slot_word\" ∧\n name ≠ \"__compat_slot_cleared\" := by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n CompilationModel.validateIdentifierShapes_field_avoidReservedCompilerPrefix hvalidate hfield\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_value\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inl rfl)\n have himm : \"__compat_value\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_packed\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inl rfl)\n have himm : \"__compat_packed\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_word\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inl rfl)\n have himm : \"__compat_slot_word\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_cleared\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inr rfl)\n have himm : \"__compat_slot_cleared\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inr rfl)\n simpa [hEq, hprefix, himm])\n\nprivate theorem scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name))) :\n scopeAvoidsReservedCompilerPrefix scope := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hmem\n have hname := hscopeNames \"__compat_value\" hmem\n have hname' :\n \"__compat_value\" ∈ fn.params.map (·.name) ∨\n \"__compat_value\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_value\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_value\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inl rfl))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_packed\" hmem\n have hname' :\n \"__compat_packed\" ∈ fn.params.map (·.name) ∨\n \"__compat_packed\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_packed\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_packed\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_word\" hmem\n have hname' :\n \"__compat_slot_word\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_word\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_word\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_word\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_cleared\" hmem\n have hname' :\n \"__compat_slot_cleared\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_cleared\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_cleared\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_cleared\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.2 rfl\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name)))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR, CompiledStmtStep spec.fields scope (.setStorage fieldName value) compiledIR := by\n by_cases halias : f.aliasSlots = []\n · refine ⟨[YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])], ?_⟩\n apply compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := ?_)\n (halias := halias)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n simpa [halias] using hwriteSlots\n · refine\n ⟨[YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))],\n ?_⟩\n apply compiledStmtStep_setStorage_aliasSlots\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (halias := halias)\n (hscopeReserved := scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n hvalidate hfn hscopeNames)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hprefix :\n StmtListScopeDiscipline\n (spec.fields.map (·.name))\n (fn.params.map (·.name))\n «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes\n (scope := List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (hvalidate := hvalidate)\n (hfn := hfn)\n (hscopeNames := ?_)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n intro name hmem\n have hscopeNames := stmtListScopeDiscipline_scope_names hprefix name hmem\n have collectStmtListBindNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListBindNames a →\n x ∈ collectStmtListBindNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListBindNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListBindNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n have collectStmtListAssignedNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListAssignedNames a →\n x ∈ collectStmtListAssignedNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListAssignedNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListAssignedNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n simp only [List.mem_append] at hscopeNames ⊢\n rcases hscopeNames with ((h | h) | h) | h\n · exact Or.inl (Or.inl (Or.inl h))\n · exact Or.inl (Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListBindNames_prefix_subset _ _ _ h)))\n · exact Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListAssignedNames_prefix_subset _ _ _ h))\n · exact Or.inr h\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -674,6 +674,32 @@\n | some _ =>\n simp [hc]\n \n+theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n+ {fields : List Field}\n+ {fieldName : String}\n+ {f : Field}\n+ {slot : Nat}\n+ {writeSlots : List Nat}\n+ {targetSlot : Nat}\n+ (hnoConflict : firstFieldWriteSlotConflict fields = none)\n+ (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n+ (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n+ (hslot : targetSlot ∈ writeSlots)\n+ (hunpacked : f.packedBits = none) :\n+ findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n+ -- Bridge result\n+ show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n+ rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n+ -- Bridge hypotheses\n+ have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n+ findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n+ have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n+ findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n+ have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n+ firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n+ exact findResolvedFieldAtSlotCopyFrom_of_member\n+ hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n+\n theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n@@ -683,7 +709,10 @@\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n- findResolvedFieldAtSlotCopy fields slot = some f := sorry\n+ findResolvedFieldAtSlotCopy fields slot = some f := by\n+ exact\n+ findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n+ hnoConflict hfind hwrite (by simp) hunpacked\n \n private theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n@@ -2690,7 +2719,11 @@\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n- ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := sorry\n+ ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n+ intro writeSlot hmem\n+ exact\n+ findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n+ hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21337,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_64"},"challenge_id":{"kind":"string","value":"46fa4d73ae1b6246"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":64,"string":"64"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"runtimeStateMatchesIR_writeUintSlots","depth":1,"n_commands":0,"n_lines":41,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm","n_chars":2453,"n_subproofs":4,"n_tactics":42,"cyclomatic":4,"n_automation":9,"n_rewrites":5,"n_structural":12,"automation_only":false,"max_nesting":16},{"theorem_name":"bindingsExactlyMatchIRVarsOnScope_writeUintSlots","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname","n_chars":113,"n_subproofs":0,"n_tactics":4,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"runtimeStateMatchesIR_writeUintSlots\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 41,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases hruntime with\\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\\n funext query\\n simp only [abstractStoreStorageOrMappingMany_eq]\\n ·\\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\\n · simp only [hmem, ↓reduceIte]\\n rcases hmem with ⟨slot, hslotMem, rfl⟩\\n have hresolved' :\\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\\n have hcontains :\\n (slots.map SourceSemantics.wordNormalize).contains\\n (SourceSemantics.wordNormalize slot) = true := by\\n rw [List.contains_eq_mem]\\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\\n have hcontains' :\\n (slots.map SourceSemantics.wordNormalize).contains\\n (slot % Verity.Core.Uint256.modulus) = true := by\\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\\n Verity.Core.UINT256_MODULUS, hcontains',\\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\\n · simp only [hmem, ↓reduceIte]\\n rw [hstorage]\\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\\n intro hq\\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\\n apply hmem\\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\",\n \"n_chars\": 2453,\n \"n_subproofs\": 4,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 9,\n \"n_rewrites\": 5,\n \"n_structural\": 12,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"bindingsExactlyMatchIRVarsOnScope_writeUintSlots\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro name hname\\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\\n hexact name hname\",\n \"n_chars\": 113,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"abstractStoreStorageOrMappingMany_eq","text":"private theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\n","fan_in":2,"n_lines":21,"n_chars":947,"n_subproofs":0,"n_tactics":11,"cyclomatic":2,"n_automation":4,"n_rewrites":2,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"abstractStoreStorageOrMappingMany_eq\",\n \"text\": \"private theorem abstractStoreStorageOrMappingMany_eq\\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\\n Compiler.Proofs.IRGeneration.IRStorageWord}\\n {slots : List Nat}\\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\\n abstractStoreStorageOrMappingMany storage slots value query =\\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\\n else storage query := by\\n induction slots generalizing storage with\\n | nil =>\\n simp [abstractStoreStorageOrMappingMany]\\n | cons slot rest ih =>\\n simp only [abstractStoreStorageOrMappingMany]\\n rw [ih]\\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\\n · subst hEq\\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 21,\n \"n_chars\": 947,\n \"n_subproofs\": 0,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 4,\n \"n_rewrites\": 2,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences","fan_in":1,"n_deps_direct":1,"n_deps_transitive":43,"n_lines":59,"n_chars":2634,"n_subproofs":0,"n_tactics":20,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences\",\n \"fan_in\": 1,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 43,\n \"n_lines\": 59,\n \"n_chars\": 2634,\n \"n_subproofs\": 0,\n \"n_tactics\": 20,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":37,"string":"37"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := sorry\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := sorry\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem compatScratch_startsWith_reserved\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__\" = true := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n\nprivate theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__immutable_\" = false := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n\nprivate theorem validateIdentifierShapes_fieldName_ne_reservedScratch\n {spec : CompilationModel}\n {name : String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hmem : name ∈ spec.fields.map (·.name)) :\n name ≠ \"__compat_value\" ∧\n name ≠ \"__compat_packed\" ∧\n name ≠ \"__compat_slot_word\" ∧\n name ≠ \"__compat_slot_cleared\" := by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n CompilationModel.validateIdentifierShapes_field_avoidReservedCompilerPrefix hvalidate hfield\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_value\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inl rfl)\n have himm : \"__compat_value\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_packed\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inl rfl)\n have himm : \"__compat_packed\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_word\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inl rfl)\n have himm : \"__compat_slot_word\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_cleared\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inr rfl)\n have himm : \"__compat_slot_cleared\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inr rfl)\n simpa [hEq, hprefix, himm])\n\nprivate theorem scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name))) :\n scopeAvoidsReservedCompilerPrefix scope := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hmem\n have hname := hscopeNames \"__compat_value\" hmem\n have hname' :\n \"__compat_value\" ∈ fn.params.map (·.name) ∨\n \"__compat_value\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_value\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_value\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inl rfl))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_packed\" hmem\n have hname' :\n \"__compat_packed\" ∈ fn.params.map (·.name) ∨\n \"__compat_packed\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_packed\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_packed\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_word\" hmem\n have hname' :\n \"__compat_slot_word\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_word\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_word\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_word\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_cleared\" hmem\n have hname' :\n \"__compat_slot_cleared\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_cleared\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_cleared\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_cleared\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.2 rfl\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name)))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR, CompiledStmtStep spec.fields scope (.setStorage fieldName value) compiledIR := by\n by_cases halias : f.aliasSlots = []\n · refine ⟨[YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])], ?_⟩\n apply compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := ?_)\n (halias := halias)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n simpa [halias] using hwriteSlots\n · refine\n ⟨[YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))],\n ?_⟩\n apply compiledStmtStep_setStorage_aliasSlots\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (halias := halias)\n (hscopeReserved := scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n hvalidate hfn hscopeNames)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hprefix :\n StmtListScopeDiscipline\n (spec.fields.map (·.name))\n (fn.params.map (·.name))\n «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes\n (scope := List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (hvalidate := hvalidate)\n (hfn := hfn)\n (hscopeNames := ?_)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n intro name hmem\n have hscopeNames := stmtListScopeDiscipline_scope_names hprefix name hmem\n have collectStmtListBindNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListBindNames a →\n x ∈ collectStmtListBindNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListBindNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListBindNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n have collectStmtListAssignedNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListAssignedNames a →\n x ∈ collectStmtListAssignedNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListAssignedNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListAssignedNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n simp only [List.mem_append] at hscopeNames ⊢\n rcases hscopeNames with ((h | h) | h) | h\n · exact Or.inl (Or.inl (Or.inl h))\n · exact Or.inl (Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListBindNames_prefix_subset _ _ _ h)))\n · exact Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListAssignedNames_prefix_subset _ _ _ h))\n · exact Or.inr h\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidateShapes : validateIdentifierShapes spec = Except.ok ())\n (hvalidateRefs : validateFunctionIdentifierReferences fn = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hparamScope : paramScopeNames fn.params = fn.params.map (·.name))\n (hprefixCore : StmtListScopeCore (spec.fields.map (·.name)) «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n (hvalidate := hvalidateShapes)\n (hfn := hfn)\n (hprefix := stmtListScopeDiscipline_of_validateFunctionIdentifierReferences_prefix\n hprefixCore hvalidateRefs hparamScope\n (by simpa [List.append_assoc] using hbody))\n (hbody := hbody)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\n-- NOTE: The _of_compileStmtList intermediate was superseded by _of_bodySurface below.\n-- Its TYPESIG_SORRY signature had a bug (missing hNotMapping parameter) and was bypassed.\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem compatScratch_startsWith_reserved\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__\" = true := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n\nprivate theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__immutable_\" = false := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n\nprivate theorem validateIdentifierShapes_fieldName_ne_reservedScratch\n {spec : CompilationModel}\n {name : String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hmem : name ∈ spec.fields.map (·.name)) :\n name ≠ \"__compat_value\" ∧\n name ≠ \"__compat_packed\" ∧\n name ≠ \"__compat_slot_word\" ∧\n name ≠ \"__compat_slot_cleared\" := by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n CompilationModel.validateIdentifierShapes_field_avoidReservedCompilerPrefix hvalidate hfield\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_value\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inl rfl)\n have himm : \"__compat_value\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_packed\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inl rfl)\n have himm : \"__compat_packed\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_word\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inl rfl)\n have himm : \"__compat_slot_word\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_cleared\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inr rfl)\n have himm : \"__compat_slot_cleared\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inr rfl)\n simpa [hEq, hprefix, himm])\n\nprivate theorem scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name))) :\n scopeAvoidsReservedCompilerPrefix scope := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hmem\n have hname := hscopeNames \"__compat_value\" hmem\n have hname' :\n \"__compat_value\" ∈ fn.params.map (·.name) ∨\n \"__compat_value\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_value\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_value\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inl rfl))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_packed\" hmem\n have hname' :\n \"__compat_packed\" ∈ fn.params.map (·.name) ∨\n \"__compat_packed\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_packed\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_packed\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_word\" hmem\n have hname' :\n \"__compat_slot_word\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_word\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_word\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_word\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_cleared\" hmem\n have hname' :\n \"__compat_slot_cleared\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_cleared\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_cleared\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_cleared\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.2 rfl\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name)))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR, CompiledStmtStep spec.fields scope (.setStorage fieldName value) compiledIR := by\n by_cases halias : f.aliasSlots = []\n · refine ⟨[YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])], ?_⟩\n apply compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := ?_)\n (halias := halias)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n simpa [halias] using hwriteSlots\n · refine\n ⟨[YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))],\n ?_⟩\n apply compiledStmtStep_setStorage_aliasSlots\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (halias := halias)\n (hscopeReserved := scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n hvalidate hfn hscopeNames)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hprefix :\n StmtListScopeDiscipline\n (spec.fields.map (·.name))\n (fn.params.map (·.name))\n «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes\n (scope := List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (hvalidate := hvalidate)\n (hfn := hfn)\n (hscopeNames := ?_)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n intro name hmem\n have hscopeNames := stmtListScopeDiscipline_scope_names hprefix name hmem\n have collectStmtListBindNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListBindNames a →\n x ∈ collectStmtListBindNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListBindNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListBindNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n have collectStmtListAssignedNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListAssignedNames a →\n x ∈ collectStmtListAssignedNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListAssignedNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListAssignedNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n simp only [List.mem_append] at hscopeNames ⊢\n rcases hscopeNames with ((h | h) | h) | h\n · exact Or.inl (Or.inl (Or.inl h))\n · exact Or.inl (Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListBindNames_prefix_subset _ _ _ h)))\n · exact Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListAssignedNames_prefix_subset _ _ _ h))\n · exact Or.inr h\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidateShapes : validateIdentifierShapes spec = Except.ok ())\n (hvalidateRefs : validateFunctionIdentifierReferences fn = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hparamScope : paramScopeNames fn.params = fn.params.map (·.name))\n (hprefixCore : StmtListScopeCore (spec.fields.map (·.name)) «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n (hvalidate := hvalidateShapes)\n (hfn := hfn)\n (hprefix := stmtListScopeDiscipline_of_validateFunctionIdentifierReferences_prefix\n hprefixCore hvalidateRefs hparamScope\n (by simpa [List.append_assoc] using hbody))\n (hbody := hbody)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\n-- NOTE: The _of_compileStmtList intermediate was superseded by _of_bodySurface below.\n-- Its TYPESIG_SORRY signature had a bug (missing hNotMapping parameter) and was bypassed.\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -804,6 +804,26 @@\n rest\n value\n \n+private theorem abstractStoreStorageOrMappingMany_eq\n+ {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n+ Compiler.Proofs.IRGeneration.IRStorageWord}\n+ {slots : List Nat}\n+ {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n+ abstractStoreStorageOrMappingMany storage slots value query =\n+ if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n+ Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n+ else storage query := by\n+ induction slots generalizing storage with\n+ | nil =>\n+ simp [abstractStoreStorageOrMappingMany]\n+ | cons slot rest ih =>\n+ simp only [abstractStoreStorageOrMappingMany]\n+ rw [ih]\n+ by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n+ · subst hEq\n+ simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n+ · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n+\n private theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n@@ -860,7 +880,47 @@\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n- storage := abstractStoreStorageOrMappingMany state.storage slots value } := sorry\n+ storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n+ rcases hruntime with\n+ ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n+ refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n+ funext query\n+ simp only [abstractStoreStorageOrMappingMany_eq]\n+ ·\n+ by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n+ · simp only [hmem, ↓reduceIte]\n+ rcases hmem with ⟨slot, hslotMem, rfl⟩\n+ have hresolved' :\n+ findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n+ simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n+ (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n+ by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n+ rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n+ have hcontains :\n+ (slots.map SourceSemantics.wordNormalize).contains\n+ (SourceSemantics.wordNormalize slot) = true := by\n+ rw [List.contains_eq_mem]\n+ exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n+ have hcontains' :\n+ (slots.map SourceSemantics.wordNormalize).contains\n+ (slot % Verity.Core.Uint256.modulus) = true := by\n+ simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n+ Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n+ simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n+ SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n+ Verity.Core.UINT256_MODULUS, hcontains',\n+ ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n+ exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n+ · simp only [hmem, ↓reduceIte]\n+ rw [hstorage]\n+ have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n+ intro hq\n+ rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n+ apply hmem\n+ exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n+ simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n+ exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n+ (encodeStorageAt_writeUintSlots_other hnotMem).symm\n \n private theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n@@ -956,7 +1016,10 @@\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n- storage := abstractStoreStorageOrMappingMany state.storage slots value } := sorry\n+ storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n+ intro name hname\n+ simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n+ hexact name hname\n \n private theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21338,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_65"},"challenge_id":{"kind":"string","value":"9252f946aca1f4a6"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":65,"string":"65"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"runtimeStateMatchesIR_writeUintSlots","depth":1,"n_commands":0,"n_lines":41,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm","n_chars":2453,"n_subproofs":4,"n_tactics":42,"cyclomatic":4,"n_automation":9,"n_rewrites":5,"n_structural":12,"automation_only":false,"max_nesting":16},{"theorem_name":"bindingsExactlyMatchIRVarsOnScope_writeUintSlots","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname","n_chars":113,"n_subproofs":0,"n_tactics":4,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"runtimeStateMatchesIR_writeUintSlots\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 41,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases hruntime with\\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\\n funext query\\n simp only [abstractStoreStorageOrMappingMany_eq]\\n ·\\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\\n · simp only [hmem, ↓reduceIte]\\n rcases hmem with ⟨slot, hslotMem, rfl⟩\\n have hresolved' :\\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\\n have hcontains :\\n (slots.map SourceSemantics.wordNormalize).contains\\n (SourceSemantics.wordNormalize slot) = true := by\\n rw [List.contains_eq_mem]\\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\\n have hcontains' :\\n (slots.map SourceSemantics.wordNormalize).contains\\n (slot % Verity.Core.Uint256.modulus) = true := by\\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\\n Verity.Core.UINT256_MODULUS, hcontains',\\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\\n · simp only [hmem, ↓reduceIte]\\n rw [hstorage]\\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\\n intro hq\\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\\n apply hmem\\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\",\n \"n_chars\": 2453,\n \"n_subproofs\": 4,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 9,\n \"n_rewrites\": 5,\n \"n_structural\": 12,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"bindingsExactlyMatchIRVarsOnScope_writeUintSlots\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro name hname\\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\\n hexact name hname\",\n \"n_chars\": 113,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"abstractStoreStorageOrMappingMany_eq","text":"private theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\n","fan_in":2,"n_lines":21,"n_chars":947,"n_subproofs":0,"n_tactics":11,"cyclomatic":2,"n_automation":4,"n_rewrites":2,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"abstractStoreStorageOrMappingMany_eq\",\n \"text\": \"private theorem abstractStoreStorageOrMappingMany_eq\\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\\n Compiler.Proofs.IRGeneration.IRStorageWord}\\n {slots : List Nat}\\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\\n abstractStoreStorageOrMappingMany storage slots value query =\\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\\n else storage query := by\\n induction slots generalizing storage with\\n | nil =>\\n simp [abstractStoreStorageOrMappingMany]\\n | cons slot rest ih =>\\n simp only [abstractStoreStorageOrMappingMany]\\n rw [ih]\\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\\n · subst hEq\\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 21,\n \"n_chars\": 947,\n \"n_subproofs\": 0,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 4,\n \"n_rewrites\": 2,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences_of_compileStmtList_of_bodySurface","fan_in":0,"n_deps_direct":1,"n_deps_transitive":44,"n_lines":62,"n_chars":3566,"n_subproofs":6,"n_tactics":28,"cyclomatic":3,"n_automation":7,"n_rewrites":0,"n_structural":5,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences_of_compileStmtList_of_bodySurface\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 44,\n \"n_lines\": 62,\n \"n_chars\": 3566,\n \"n_subproofs\": 6,\n \"n_tactics\": 28,\n \"cyclomatic\": 3,\n \"n_automation\": 7,\n \"n_rewrites\": 0,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":38,"string":"38"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := sorry\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := sorry\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem compatScratch_startsWith_reserved\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__\" = true := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n\nprivate theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__immutable_\" = false := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n\nprivate theorem validateIdentifierShapes_fieldName_ne_reservedScratch\n {spec : CompilationModel}\n {name : String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hmem : name ∈ spec.fields.map (·.name)) :\n name ≠ \"__compat_value\" ∧\n name ≠ \"__compat_packed\" ∧\n name ≠ \"__compat_slot_word\" ∧\n name ≠ \"__compat_slot_cleared\" := by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n CompilationModel.validateIdentifierShapes_field_avoidReservedCompilerPrefix hvalidate hfield\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_value\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inl rfl)\n have himm : \"__compat_value\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_packed\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inl rfl)\n have himm : \"__compat_packed\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_word\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inl rfl)\n have himm : \"__compat_slot_word\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_cleared\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inr rfl)\n have himm : \"__compat_slot_cleared\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inr rfl)\n simpa [hEq, hprefix, himm])\n\nprivate theorem scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name))) :\n scopeAvoidsReservedCompilerPrefix scope := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hmem\n have hname := hscopeNames \"__compat_value\" hmem\n have hname' :\n \"__compat_value\" ∈ fn.params.map (·.name) ∨\n \"__compat_value\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_value\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_value\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inl rfl))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_packed\" hmem\n have hname' :\n \"__compat_packed\" ∈ fn.params.map (·.name) ∨\n \"__compat_packed\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_packed\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_packed\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_word\" hmem\n have hname' :\n \"__compat_slot_word\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_word\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_word\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_word\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_cleared\" hmem\n have hname' :\n \"__compat_slot_cleared\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_cleared\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_cleared\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_cleared\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.2 rfl\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name)))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR, CompiledStmtStep spec.fields scope (.setStorage fieldName value) compiledIR := by\n by_cases halias : f.aliasSlots = []\n · refine ⟨[YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])], ?_⟩\n apply compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := ?_)\n (halias := halias)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n simpa [halias] using hwriteSlots\n · refine\n ⟨[YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))],\n ?_⟩\n apply compiledStmtStep_setStorage_aliasSlots\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (halias := halias)\n (hscopeReserved := scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n hvalidate hfn hscopeNames)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hprefix :\n StmtListScopeDiscipline\n (spec.fields.map (·.name))\n (fn.params.map (·.name))\n «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes\n (scope := List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (hvalidate := hvalidate)\n (hfn := hfn)\n (hscopeNames := ?_)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n intro name hmem\n have hscopeNames := stmtListScopeDiscipline_scope_names hprefix name hmem\n have collectStmtListBindNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListBindNames a →\n x ∈ collectStmtListBindNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListBindNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListBindNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n have collectStmtListAssignedNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListAssignedNames a →\n x ∈ collectStmtListAssignedNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListAssignedNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListAssignedNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n simp only [List.mem_append] at hscopeNames ⊢\n rcases hscopeNames with ((h | h) | h) | h\n · exact Or.inl (Or.inl (Or.inl h))\n · exact Or.inl (Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListBindNames_prefix_subset _ _ _ h)))\n · exact Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListAssignedNames_prefix_subset _ _ _ h))\n · exact Or.inr h\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidateShapes : validateIdentifierShapes spec = Except.ok ())\n (hvalidateRefs : validateFunctionIdentifierReferences fn = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hparamScope : paramScopeNames fn.params = fn.params.map (·.name))\n (hprefixCore : StmtListScopeCore (spec.fields.map (·.name)) «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n (hvalidate := hvalidateShapes)\n (hfn := hfn)\n (hprefix := stmtListScopeDiscipline_of_validateFunctionIdentifierReferences_prefix\n hprefixCore hvalidateRefs hparamScope\n (by simpa [List.append_assoc] using hbody))\n (hbody := hbody)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\n-- NOTE: The _of_compileStmtList intermediate was superseded by _of_bodySurface below.\n-- Its TYPESIG_SORRY signature had a bug (missing hNotMapping parameter) and was bypassed.\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences_of_compileStmtList_of_bodySurface\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {bodyIR : List YulStmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidateShapes : validateIdentifierShapes spec = Except.ok ())\n (hvalidateRefs : validateFunctionIdentifierReferences fn = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hparamScope : paramScopeNames fn.params = fn.params.map (·.name))\n (hbodySurface : stmtListTouchesUnsupportedContractSurface fn.body = false)\n (hbodyCompile :\n CompilationModel.compileStmtList\n spec.fields [] [] .calldata [] false (fn.params.map (·.name)) [] fn.body =\n Except.ok bodyIR)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n have hprefixCore : StmtListScopeCore (spec.fields.map (·.name)) «prefix» :=\n stmtListScopeCore_prefix_of_compileStmtList_ok_of_stmtListTouchesUnsupportedContractSurface\n (by simpa [hbody] using hbodySurface) (by simpa [hbody] using hbodyCompile)\n have hstmtSurface :\n stmtTouchesUnsupportedContractSurface (.setStorage fieldName value) = false :=\n stmtTouchesUnsupportedContractSurface_of_stmtListTouchesUnsupportedContractSurface_append_cons\n (by simpa [hbody] using hbodySurface)\n have hvalueCore : FunctionBody.ExprCompileCore value :=\n exprCompileCore_of_exprTouchesUnsupportedContractSurface_eq_false\n (by simpa [stmtTouchesUnsupportedContractSurface] using hstmtSurface)\n have hinScope := exprBoundNamesInScope_setStorage_of_validateFunctionIdentifierReferences\n hprefixCore hvalueCore hvalidateRefs hparamScope hbody\n have hNotMapping : isMapping spec.fields fieldName = false := by\n rcases compileStmt_ok_of_compileStmtList_append_cons\n (by simpa [hbody] using hbodyCompile) with ⟨stmtIR, hstmt⟩\n exact isMapping_false_of_compileStmt_setStorage_ok hstmt\n have hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields := by\n intro name maxFields hty\n rcases compileStmt_ok_of_compileStmtList_append_cons\n (by simpa [hbody] using hbodyCompile) with ⟨stmtIR, hstmt⟩\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hty, hvalueIR, pure, Pure.pure, Except.pure,\n Bind.bind, Except.bind] at hstmt\n exact compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences\n hvalidateShapes hvalidateRefs hfn hparamScope hprefixCore hbody hvalueCore hinScope\n hfind hwriteSlots hunpacked hnoConflict hnotAddr hnotDyn hnotTransient\n hNotMapping hNotAdt hvalueIR\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nprivate theorem encodeStorageAt_writeUintSlots_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slots : List Nat}\n {query value : Nat}\n (hnotMem : query ∉ slots.map SourceSemantics.wordNormalize) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world slots value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintSlots]\n rw [show (slots.map SourceSemantics.wordNormalize).contains query = false from by\n simpa using hnotMem]\n simp\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n abstractStoreStorageOrMappingMany storage slots value query =\n if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n else storage query := by\n induction slots generalizing storage with\n | nil =>\n simp [abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n simp only [abstractStoreStorageOrMappingMany]\n rw [ih]\n by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n · subst hEq\n simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeUintSlots\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : ∀ slot ∈ slots, findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n simp only [abstractStoreStorageOrMappingMany_eq]\n ·\n by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n · simp only [hmem, ↓reduceIte]\n rcases hmem with ⟨slot, hslotMem, rfl⟩\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n have hcontains :\n (slots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) = true := by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n have hcontains' :\n (slots.map SourceSemantics.wordNormalize).contains\n (slot % Verity.Core.Uint256.modulus) = true := by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, hcontains',\n ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n · simp only [hmem, ↓reduceIte]\n rw [hstorage]\n have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n intro hq\n rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n apply hmem\n exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_other hnotMem).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlots\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slots : List Nat}\n {value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n intro name hname\n simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.length + fuel + 1) state\n (slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name]))) =\n .continue\n { state with\n storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n induction slots generalizing state fuel with\n | nil =>\n simp [execIRStmts, abstractStoreStorageOrMappingMany]\n | cons slot rest ih =>\n let nextState :=\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value }\n have hstmt :\n execIRStmt (rest.length + fuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident name])) =\n .continue nextState := by\n apply execIRStmt_sstore_lit_expr_succ_of_eval\n simp only [evalIRExpr]; exact hvalue\n have hvalueNext : IRState.getVar nextState name = value := by\n simp only [nextState, IRState.getVar]; exact hvalue\n have htail :=\n ih (fuel := fuel) (state := nextState) hvalueNext\n simp only [execIRStmts, List.map, List.length_cons]\n have hfuel : rest.length + 1 + fuel = rest.length + fuel + 1 := by omega\n rw [hfuel, hstmt]\n simp only [abstractStoreStorageOrMappingMany]\n convert htail using 2\n\nprivate theorem execIRStmts_let_then_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (tempName : String)\n (valueIR : YulExpr)\n (value : Nat)\n (hvalue : evalIRExpr state valueIR = some value) :\n execIRStmts (slots.length + fuel + 2) state\n (YulStmt.let_ tempName valueIR ::\n slots.map (fun slot =>\n YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, YulExpr.ident tempName]))) =\n .continue\n { state.setVar tempName value with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar tempName value).storage\n slots\n value } := by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ tempName valueIR) =\n .continue (state.setVar tempName value) := by\n simp [execIRStmt, hvalue]\n have hslots :=\n execIRStmts_sstore_lit_ident_slots_continue\n fuel\n (state.setVar tempName value)\n slots\n tempName\n value\n (by simp [IRState.getVar, IRState.setVar])\n simpa [execIRStmts, hlet] using hslots\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem compatValue_not_mem_scope_of_reservedPrefix\n {scope : List String}\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope) :\n \"__compat_value\" ∉ scope := by\n exact hscopeReserved.1\n\nprivate theorem compatScratch_startsWith_reserved\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__\" = true := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__\".length) \"__\".toSubstring = true\n simp [Substring.beq, String.toSubstring, Substring.take]\n constructor\n · rfl\n · unfold String.substrEq\n simp\n constructor\n · decide\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n right\n constructor\n · rfl\n · unfold String.substrEq.loop\n simp\n left\n decide\n\nprivate theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.startsWith \"__immutable_\" = false := by\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_value\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_packed\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n rcases h with h | h\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_word\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n · subst h\n unfold String.startsWith\n change Substring.beq (\"__compat_slot_cleared\".toSubstring.take \"__immutable_\".length)\n \"__immutable_\".toSubstring = false\n simp [Substring.beq, String.toSubstring, Substring.take]\n intro hlen\n unfold String.substrEq\n simp\n intro h1\n intro h2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar2\n unfold String.substrEq.loop\n simp\n constructor\n · decide\n · intro hchar3\n cases hchar3\n\nprivate theorem validateIdentifierShapes_fieldName_ne_reservedScratch\n {spec : CompilationModel}\n {name : String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hmem : name ∈ spec.fields.map (·.name)) :\n name ≠ \"__compat_value\" ∧\n name ≠ \"__compat_packed\" ∧\n name ≠ \"__compat_slot_word\" ∧\n name ≠ \"__compat_slot_cleared\" := by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n CompilationModel.validateIdentifierShapes_field_avoidReservedCompilerPrefix hvalidate hfield\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_value\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inl rfl)\n have himm : \"__compat_value\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_packed\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inl rfl)\n have himm : \"__compat_packed\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_word\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inl rfl)\n have himm : \"__compat_slot_word\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inl rfl)\n simpa [hEq, hprefix, himm])\n · intro hEq\n exact hreserved (by\n have hprefix : \"__compat_slot_cleared\".startsWith \"__\" = true := by\n exact compatScratch_startsWith_reserved (Or.inr <| Or.inr <| Or.inr rfl)\n have himm : \"__compat_slot_cleared\".startsWith \"__immutable_\" = false := by\n exact compatScratch_not_internalImmutable (Or.inr <| Or.inr <| Or.inr rfl)\n simpa [hEq, hprefix, himm])\n\nprivate theorem scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name))) :\n scopeAvoidsReservedCompilerPrefix scope := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro hmem\n have hname := hscopeNames \"__compat_value\" hmem\n have hname' :\n \"__compat_value\" ∈ fn.params.map (·.name) ∨\n \"__compat_value\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_value\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_value\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inl rfl))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inl rfl))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_packed\" hmem\n have hname' :\n \"__compat_packed\" ∈ fn.params.map (·.name) ∨\n \"__compat_packed\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_packed\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_packed\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inl rfl)))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_word\" hmem\n have hname' :\n \"__compat_slot_word\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_word\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_word\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_word\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inl rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.1 rfl\n · intro hmem\n have hname := hscopeNames \"__compat_slot_cleared\" hmem\n have hname' :\n \"__compat_slot_cleared\" ∈ fn.params.map (·.name) ∨\n \"__compat_slot_cleared\" ∈ collectStmtListBindNames fn.body ∨\n \"__compat_slot_cleared\" ∈ collectStmtListAssignedNames fn.body ∨\n \"__compat_slot_cleared\" ∈ spec.fields.map (·.name) := by\n simpa [List.mem_append, or_assoc] using hname\n rcases hname' with hparam | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionParams_avoidReservedCompilerPrefix\n hvalidate hfn hparam) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hlocal | hrest\n · exact\n (CompilationModel.validateIdentifierShapes_functionLocals_avoidReservedCompilerPrefix\n hvalidate hfn hlocal) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n rcases hrest with hassign | hfield\n · exact\n (CompilationModel.validateIdentifierShapes_functionAssignTargets_avoidReservedCompilerPrefix\n hvalidate hfn hassign) (compatScratch_startsWith_reserved (Or.inr (Or.inr (Or.inr rfl))))\n · exact (validateIdentifierShapes_fieldName_ne_reservedScratch hvalidate hfield).2.2.2 rfl\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_aliasSlots\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some (slot :: f.aliasSlots))\n (halias : f.aliasSlots ≠ [])\n (hscopeReserved : scopeAvoidsReservedCompilerPrefix scope)\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))] where\n compileOk := by\n cases hty : f.ty with\n | adt name maxFields =>\n exact False.elim (hNotAdt name maxFields hty)\n | uint256 | address | dynamicArray | mappingTyped | mappingStruct | mappingStruct2 =>\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, halias, hunpacked, hnotTransient, hvalueIR, hty,\n pure, Except.pure, Bind.bind, Except.bind]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let slots := slot :: f.aliasSlots\n let blockBody :=\n [YulStmt.let_ \"__compat_value\" valueIR] ++\n slots.map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"]))\n let compiledIR := [YulStmt.block blockBody]\n have heval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at heval\n simp [Except.toOption] at heval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at heval\n · simp [hIRValue, Option.bind] at heval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n heval.symm\n have hvalueEval : evalIRExpr state valueIR = some valueNat := hIRValue\n -- Prove sizeOf of any YulStmt list ≥ length + 1\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : slots.length + 2 ≤ extraFuel := by\n have hslack' : sizeOf compiledIR - compiledIR.length ≤ extraFuel := by\n simpa [compiledIR] using hslack\n have hlen : compiledIR.length = 1 := by simp [compiledIR]\n -- blockBody.length = 1 + slots.length (let_ + map)\n have hBodyLen : blockBody.length = 1 + slots.length := by\n simp [blockBody, slots]; omega\n have hBodyBound := hSizeOfListBound blockBody\n -- sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1\n have hCompSizeOf : sizeOf compiledIR = 1 + sizeOf (YulStmt.block blockBody) + 1 := by\n dsimp only [compiledIR]; rfl\n -- sizeOf (YulStmt.block body) ≥ 1 + sizeOf body\n have hBlockSizeOf : 1 + sizeOf blockBody ≤ sizeOf (YulStmt.block blockBody) := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n let bodyExtraFuel := extraFuel - (slots.length + 2)\n have hbodyFuelEq : slots.length + bodyExtraFuel + 2 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hresolvedSlots :\n ∀ writeSlot ∈ slots, findResolvedFieldAtSlotCopy fields writeSlot = some f := by\n intro writeSlot hmem\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwriteSlots hmem hunpacked\n have hbody :\n execIRStmts extraFuel state blockBody =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have := execIRStmts_let_then_sstore_lit_ident_slots_continue\n bodyExtraFuel state slots \"__compat_value\" valueIR valueNat hvalueEval\n rw [hbodyFuelEq] at this\n simpa [blockBody, slots] using this\n have hwhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat } := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state\n { state.setVar \"__compat_value\" valueNat with\n storage :=\n abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage\n slots\n valueNat }\n blockBody\n hbody\n convert hblock using 2\n simp [compiledIR]; omega\n -- Prove value bound\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n -- Source execution\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue\n { runtime with\n world := SourceSemantics.writeUintSlots runtime.world (slot :: f.aliasSlots) valueNat } := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, slots]\n -- Scope inclusion\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n -- Runtime state match\n have hruntimeSet :\n FunctionBody.runtimeStateMatchesIR fields runtime (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntime\n have hruntime' : FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots valueNat }\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n runtimeStateMatchesIR_writeUintSlots hruntimeSet hresolvedSlots hnotAddr hnotDyn hvalueLt\n -- Bindings match\n have hexactSet :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings\n (state.setVar \"__compat_value\" valueNat) :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n hexact (compatValue_not_mem_scope_of_reservedPrefix hscopeReserved)\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setStorage fieldName value)) runtime.bindings\n { (state.setVar \"__compat_value\" valueNat) with\n storage := abstractStoreStorageOrMappingMany\n (state.setVar \"__compat_value\" valueNat).storage slots valueNat } :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlots hexactSet) hincl\n refine ⟨_, _, hSrcExec, hwhole, ?_⟩\n simp [stmtStepMatchesIRExec, slots]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hscopeNames :\n ∀ name, name ∈ scope →\n name ∈\n (fn.params.map (·.name) ++\n collectStmtListBindNames fn.body ++\n collectStmtListAssignedNames fn.body ++\n spec.fields.map (·.name)))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR, CompiledStmtStep spec.fields scope (.setStorage fieldName value) compiledIR := by\n by_cases halias : f.aliasSlots = []\n · refine ⟨[YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])], ?_⟩\n apply compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := ?_)\n (halias := halias)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n simpa [halias] using hwriteSlots\n · refine\n ⟨[YulStmt.block\n ([YulStmt.let_ \"__compat_value\" valueIR] ++\n (slot :: f.aliasSlots).map (fun writeSlot =>\n YulStmt.exprStmt\n (YulExpr.call \"sstore\" [YulExpr.lit writeSlot, YulExpr.ident \"__compat_value\"])))],\n ?_⟩\n apply compiledStmtStep_setStorage_aliasSlots\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (halias := halias)\n (hscopeReserved := scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes\n hvalidate hfn hscopeNames)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidate : validateIdentifierShapes spec = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hprefix :\n StmtListScopeDiscipline\n (spec.fields.map (·.name))\n (fn.params.map (·.name))\n «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes\n (scope := List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (hvalidate := hvalidate)\n (hfn := hfn)\n (hscopeNames := ?_)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n intro name hmem\n have hscopeNames := stmtListScopeDiscipline_scope_names hprefix name hmem\n have collectStmtListBindNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListBindNames a →\n x ∈ collectStmtListBindNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListBindNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListBindNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n have collectStmtListAssignedNames_prefix_subset :\n ∀ (a b : List Stmt), ∀ x, x ∈ collectStmtListAssignedNames a →\n x ∈ collectStmtListAssignedNames (a ++ b) := by\n intro a b x hx\n induction a with\n | nil => simp [collectStmtListAssignedNames] at hx\n | cons s rest ih =>\n simp only [collectStmtListAssignedNames, List.mem_append, List.cons_append] at hx ⊢\n rcases hx with h | h\n · exact Or.inl h\n · exact Or.inr (ih h)\n simp only [List.mem_append] at hscopeNames ⊢\n rcases hscopeNames with ((h | h) | h) | h\n · exact Or.inl (Or.inl (Or.inl h))\n · exact Or.inl (Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListBindNames_prefix_subset _ _ _ h)))\n · exact Or.inl (Or.inr\n (by rw [hbody]; exact collectStmtListAssignedNames_prefix_subset _ _ _ h))\n · exact Or.inr h\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidateShapes : validateIdentifierShapes spec = Except.ok ())\n (hvalidateRefs : validateFunctionIdentifierReferences fn = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hparamScope : paramScopeNames fn.params = fn.params.map (·.name))\n (hprefixCore : StmtListScopeCore (spec.fields.map (·.name)) «prefix»)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope :\n FunctionBody.exprBoundNamesInScope\n value\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»))\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping spec.fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n apply compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline\n (hvalidate := hvalidateShapes)\n (hfn := hfn)\n (hprefix := stmtListScopeDiscipline_of_validateFunctionIdentifierReferences_prefix\n hprefixCore hvalidateRefs hparamScope\n (by simpa [List.append_assoc] using hbody))\n (hbody := hbody)\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := hwriteSlots)\n (hunpacked := hunpacked)\n (hnoConflict := hnoConflict)\n (hnotAddr := hnotAddr)\n (hnotDyn := hnotDyn)\n (hnotTransient := hnotTransient)\n (hNotMapping := hNotMapping)\n (hNotAdt := hNotAdt)\n (hvalueIR := hvalueIR)\n\n-- NOTE: The _of_compileStmtList intermediate was superseded by _of_bodySurface below.\n-- Its TYPESIG_SORRY signature had a bug (missing hNotMapping parameter) and was bypassed.\n\ntheorem compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences_of_compileStmtList_of_bodySurface\n {spec : CompilationModel}\n {fn : FunctionSpec}\n {«prefix» «suffix» : List Stmt}\n {bodyIR : List YulStmt}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hvalidateShapes : validateIdentifierShapes spec = Except.ok ())\n (hvalidateRefs : validateFunctionIdentifierReferences fn = Except.ok ())\n (hfn : fn ∈ spec.functions)\n (hparamScope : paramScopeNames fn.params = fn.params.map (·.name))\n (hbodySurface : stmtListTouchesUnsupportedContractSurface fn.body = false)\n (hbodyCompile :\n CompilationModel.compileStmtList\n spec.fields [] [] .calldata [] false (fn.params.map (·.name)) [] fn.body =\n Except.ok bodyIR)\n (hbody : fn.body = «prefix» ++ .setStorage fieldName value :: «suffix»)\n (hfind : findFieldWithResolvedSlot spec.fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots spec.fields fieldName = some (slot :: f.aliasSlots))\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict spec.fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hvalueIR : CompilationModel.compileExpr spec.fields .calldata value = Except.ok valueIR) :\n ∃ compiledIR,\n CompiledStmtStep spec.fields\n (List.foldl stmtNextScope (fn.params.map (·.name)) «prefix»)\n (.setStorage fieldName value)\n compiledIR := by\n have hprefixCore : StmtListScopeCore (spec.fields.map (·.name)) «prefix» :=\n stmtListScopeCore_prefix_of_compileStmtList_ok_of_stmtListTouchesUnsupportedContractSurface\n (by simpa [hbody] using hbodySurface) (by simpa [hbody] using hbodyCompile)\n have hstmtSurface :\n stmtTouchesUnsupportedContractSurface (.setStorage fieldName value) = false :=\n stmtTouchesUnsupportedContractSurface_of_stmtListTouchesUnsupportedContractSurface_append_cons\n (by simpa [hbody] using hbodySurface)\n have hvalueCore : FunctionBody.ExprCompileCore value :=\n exprCompileCore_of_exprTouchesUnsupportedContractSurface_eq_false\n (by simpa [stmtTouchesUnsupportedContractSurface] using hstmtSurface)\n have hinScope := exprBoundNamesInScope_setStorage_of_validateFunctionIdentifierReferences\n hprefixCore hvalueCore hvalidateRefs hparamScope hbody\n have hNotMapping : isMapping spec.fields fieldName = false := by\n rcases compileStmt_ok_of_compileStmtList_append_cons\n (by simpa [hbody] using hbodyCompile) with ⟨stmtIR, hstmt⟩\n exact isMapping_false_of_compileStmt_setStorage_ok hstmt\n have hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields := by\n intro name maxFields hty\n rcases compileStmt_ok_of_compileStmtList_append_cons\n (by simpa [hbody] using hbodyCompile) with ⟨stmtIR, hstmt⟩\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hty, hvalueIR, pure, Pure.pure, Except.pure,\n Bind.bind, Except.bind] at hstmt\n exact compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences\n hvalidateShapes hvalidateRefs hfn hparamScope hprefixCore hbody hvalueCore hinScope\n hfind hwriteSlots hunpacked hnoConflict hnotAddr hnotDyn hnotTransient\n hNotMapping hNotAdt hvalueIR\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -804,6 +804,26 @@\n rest\n value\n \n+private theorem abstractStoreStorageOrMappingMany_eq\n+ {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n+ Compiler.Proofs.IRGeneration.IRStorageWord}\n+ {slots : List Nat}\n+ {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :\n+ abstractStoreStorageOrMappingMany storage slots value query =\n+ if ∃ slot ∈ slots, query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot then\n+ Compiler.Proofs.IRGeneration.IRStorageWord.ofNat value\n+ else storage query := by\n+ induction slots generalizing storage with\n+ | nil =>\n+ simp [abstractStoreStorageOrMappingMany]\n+ | cons slot rest ih =>\n+ simp only [abstractStoreStorageOrMappingMany]\n+ rw [ih]\n+ by_cases hEq : query = Compiler.Proofs.IRGeneration.IRStorageSlot.ofNat slot\n+ · subst hEq\n+ simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n+ · simp [Compiler.Proofs.abstractStoreStorageOrMapping_eq, hEq]\n+\n private theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n@@ -860,7 +880,47 @@\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world slots value }\n { state with\n- storage := abstractStoreStorageOrMappingMany state.storage slots value } := sorry\n+ storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n+ rcases hruntime with\n+ ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n+ refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n+ funext query\n+ simp only [abstractStoreStorageOrMappingMany_eq]\n+ ·\n+ by_cases hmem : ∃ slot ∈ slots, query = IRStorageSlot.ofNat slot\n+ · simp only [hmem, ↓reduceIte]\n+ rcases hmem with ⟨slot, hslotMem, rfl⟩\n+ have hresolved' :\n+ findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n+ simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n+ (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n+ by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved slot hslotMem)\n+ rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n+ have hcontains :\n+ (slots.map SourceSemantics.wordNormalize).contains\n+ (SourceSemantics.wordNormalize slot) = true := by\n+ rw [List.contains_eq_mem]\n+ exact decide_eq_true (List.mem_map.mpr ⟨slot, hslotMem, rfl⟩)\n+ have hcontains' :\n+ (slots.map SourceSemantics.wordNormalize).contains\n+ (slot % Verity.Core.Uint256.modulus) = true := by\n+ simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n+ Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.modulus] using hcontains\n+ simp only [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n+ SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n+ Verity.Core.UINT256_MODULUS, hcontains',\n+ ↓reduceIte, Verity.Core.Uint256.val_ofNat]\n+ exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (Nat.mod_eq_of_lt hvalue).symm\n+ · simp only [hmem, ↓reduceIte]\n+ rw [hstorage]\n+ have hnotMem : query.toNat ∉ slots.map SourceSemantics.wordNormalize := by\n+ intro hq\n+ rcases List.mem_map.mp hq with ⟨slot, hslotMem, hslotEq⟩\n+ apply hmem\n+ exact ⟨slot, hslotMem, IRStorageSlot.eq_of_toNat_eq (by\n+ simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using hslotEq.symm)⟩\n+ exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n+ (encodeStorageAt_writeUintSlots_other hnotMem).symm\n \n private theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n@@ -956,7 +1016,10 @@\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n- storage := abstractStoreStorageOrMappingMany state.storage slots value } := sorry\n+ storage := abstractStoreStorageOrMappingMany state.storage slots value } := by\n+ intro name hname\n+ simpa [IRState.getVar, abstractStoreStorageOrMappingMany_eq] using\n+ hexact name hname\n \n private theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21339,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_66"},"challenge_id":{"kind":"string","value":"6ce611d588899001"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":66,"string":"66"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":14,"string":"14"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compiledStmtStep_mstore_single","depth":1,"n_commands":0,"n_lines":7,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n hoffsetIRInternal, hvalueIRInternal, Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_mstore_single_preserves\n hcoreOffset hinScopeOffset hcoreValue hinScopeValue hoffsetIR hvalueIR","n_chars":440,"n_subproofs":2,"n_tactics":7,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_tstore_single","depth":1,"n_commands":0,"n_lines":7,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n hoffsetIRInternal, hvalueIRInternal, Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_tstore_single_preserves\n hcoreOffset hinScopeOffset hcoreValue hinScopeValue hoffsetIR hvalueIR","n_chars":440,"n_subproofs":2,"n_tactics":7,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMappingUint_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR","n_chars":729,"n_subproofs":2,"n_tactics":11,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compileExprList_core_ok","depth":1,"n_commands":0,"n_lines":19,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction exprs with\n | nil =>\n exact ⟨[], by\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\n pure, Except.pure]⟩\n | cons expr rest ih =>\n have hhead : FunctionBody.ExprCompileCore expr := hcore expr (by simp)\n have htail : ∀ e ∈ rest, FunctionBody.ExprCompileCore e := by\n intro e he\n exact hcore e (by simp [he])\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hhead with ⟨exprIR, hexprIR⟩\n rcases ih htail with ⟨restIR, hrestIR⟩\n have hexprIRInternal := compileExprWithInternals_nil_ok hexprIR\n have hrestIRInternal := compileExprListWithInternals_nil_ok hrestIR\n exact ⟨exprIR :: restIR, by\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\n hexprIRInternal, hrestIRInternal, bind, Except.bind, pure, Except.pure]\n ⟩","n_chars":930,"n_subproofs":4,"n_tactics":19,"cyclomatic":4,"n_automation":4,"n_rewrites":0,"n_structural":7,"automation_only":false,"max_nesting":10},{"theorem_name":"eval_compileExprList_core_of_scope","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction exprs generalizing exprIRs with\n | nil =>\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals] at hcompiled\n cases hcompiled\n exact ⟨[], rfl, .nil⟩\n | cons expr rest ih =>\n have hhead : FunctionBody.ExprCompileCore expr := hcore expr (by simp)\n have htail :\n ∀ expr' ∈ rest, FunctionBody.ExprCompileCore expr' := by\n intro expr' hexpr'\n exact hcore expr' (by simp [hexpr'])\n have htailScope :\n ∀ expr' ∈ rest, FunctionBody.exprBoundNamesInScope expr' scope := by\n intro expr' hexpr'\n exact hinScope expr' (by simp [hexpr'])\n rcases compileExprList_core_ok (fields := fields) htail with ⟨restIRs, hrestIRs⟩\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hhead with ⟨exprIR, hexprIR⟩\n have hexprIRInternal := compileExprWithInternals_nil_ok hexprIR\n have hrestIRsInternal := compileExprListWithInternals_nil_ok hrestIRs\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\n hexprIRInternal, hrestIRsInternal] at hcompiled\n injection hcompiled with hcompiledTail\n subst hcompiledTail\n rcases eval_compileExpr_core_some_of_scope\n (expr := expr) (exprIR := exprIR) hhead hexact (hinScope expr (by simp))\n hbounded hscope hruntime hexprIR with\n ⟨headVal, hheadVal, hheadEval⟩\n rcases ih htail htailScope hrestIRs with\n ⟨restVals, hrestVals, hrestEval⟩\n refine ⟨headVal :: restVals, ?_, ?_⟩\n · simp [SourceSemantics.evalExprList, hheadVal, hrestVals]\n · exact .cons hheadEval hrestEval","n_chars":1688,"n_subproofs":5,"n_tactics":33,"cyclomatic":7,"n_automation":8,"n_rewrites":1,"n_structural":13,"automation_only":false,"max_nesting":10},{"theorem_name":"compiledStmtStep_setMappingChain_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRsInternal := compileExprListWithInternals_nil_ok hkeyIRs\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMappingChain,\n hmapping, hwriteSlots, hkeyIRsInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMappingChain_singleSlot_of_slotSafety_preserves\n hcoreKeys hinScopeKeys hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIRs hvalueIR","n_chars":739,"n_subproofs":2,"n_tactics":11,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMapping_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMapping_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR","n_chars":725,"n_subproofs":2,"n_tactics":11,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMappingWord_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMappingWord_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR","n_chars":729,"n_subproofs":2,"n_tactics":11,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":14,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingPackedSlotWrite,\n hmapping, hpacked, hwriteSlots, hkeyIRInternal, hvalueIRInternal, Bool.not_true, bne_self_eq_false,\n ite_false, ite_true, pure, Except.pure, bind, Except.bind]\n simp [hfind, fieldLoadBuiltin, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue\n hcompatValue hcompatPacked hcompatSlotWord hcompatSlotCleared\n hpacked hwriteSlots hslotSafety hkeyIR hvalueIR","n_chars":945,"n_subproofs":2,"n_tactics":14,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setStructMember_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":13,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember,\n CompilationModel.compileMappingSlotWrite, hmapping, hnotMapping2, hmembers, hmember,\n hwriteSlots, hkeyIRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setStructMember_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue hmembers hmember hwriteSlots\n hslotSafety hkeyIR hvalueIR","n_chars":831,"n_subproofs":2,"n_tactics":13,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMapping2_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":13,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMapping2,\n hmapping2, hwriteSlots, hkey1IRInternal, hkey2IRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMapping2_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR","n_chars":848,"n_subproofs":3,"n_tactics":13,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":13,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMapping2Word,\n hmapping2, hwriteSlots, hkey1IRInternal, hkey2IRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR","n_chars":856,"n_subproofs":3,"n_tactics":13,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setStructMember2_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":14,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember2,\n hmapping2, hmembers, hmember, hwriteSlots, hkey1IRInternal, hkey2IRInternal,\n hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hmembers hmember hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR","n_chars":900,"n_subproofs":3,"n_tactics":14,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_ite","depth":1,"n_commands":0,"n_lines":237,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcond with ⟨condIR, hcondIR⟩\n rcases FunctionBody.compileStmtList_terminal_core_ok\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := thenBranch)\n hthen with ⟨thenIR, hthenIR⟩\n rcases FunctionBody.compileStmtList_terminal_core_ok\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := elseBranch)\n helse with ⟨elseIR, helseIR⟩\n have helseNonempty : elseBranch.isEmpty = false := by\n cases elseBranch with\n | nil => exfalso; exact FunctionBody.stmtListTerminalCore_ne_nil helse rfl\n | cons => simp\n let tempName :=\n CompilationModel.pickFreshName \"__ite_cond\"\n (scope ++ collectExprNames cond ++\n collectStmtListNames thenBranch ++ collectStmtListNames elseBranch)\n let compiledIR :=\n [YulStmt.block\n [ YulStmt.let_ tempName condIR\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\n , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]]\n refine ⟨compiledIR, ?_⟩\n refine\n { compileOk := ?_\n preserves := ?_ }\n · show CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (.ite cond thenBranch elseBranch) = Except.ok compiledIR\n have hcondIRInternal := compileExprWithInternals_nil_ok hcondIR\n unfold CompilationModel.compileStmt CompilationModel.compileStmtWithFork\n simp [FunctionBody.compileStmtListWithFork_cancun_eq_compileStmtList,\n hcondIRInternal, hthenIR, helseIR, Except.bind, helseNonempty]\n simp [compiledIR, tempName, List.append_assoc, Bind.bind, Except.bind,\n Pure.pure, Except.pure]\n · intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n set wholeExtraFuel := extraFuel - (sizeOf compiledIR - compiledIR.length) with hWF\n have hsizeOf_eq : sizeOf compiledIR = 1 + sizeOf (YulStmt.block\n [ YulStmt.let_ tempName condIR\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\n , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]) + 1 := by\n rfl\n have hlength_eq : compiledIR.length = 1 := by rfl\n have hwholeFuel :\n compiledIR.length + extraFuel + 1 =\n sizeOf compiledIR + wholeExtraFuel + 1 := by\n rw [hWF, hsizeOf_eq, hlength_eq]\n have : sizeOf compiledIR - compiledIR.length ≤ extraFuel := hslack\n rw [hsizeOf_eq, hlength_eq] at this\n omega\n have hpresent : FunctionBody.exprBoundNamesPresent cond runtime.bindings :=\n FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope\n -- Extract the Nat condition value via the eval bridge\n have heval := FunctionBody.eval_compileExpr_core_of_scope\n hcond hexact hinScope hbounded hpresent hruntime\n rw [hcondIR] at heval; simp [Except.toOption] at heval\n rcases hCondIRVal : evalIRExpr state condIR with _ | condVal\n · simp [hCondIRVal, Option.bind] at heval\n · simp [hCondIRVal, Option.bind] at heval\n have hCondSrc : SourceSemantics.evalExpr fields runtime cond = some condVal :=\n heval.symm\n have hcondEval : evalIRExpr state condIR = some condVal := hCondIRVal\n by_cases hcondZero : condVal = 0\n · -- Condition is zero → take else branch\n have hBindIte :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n (scope := scope) (inScopeNames := scope)\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n have hRuntimeIte :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := tempName) (value := condVal) hruntime\n have hElse6 : sizeOf elseIR + 6 ≤ sizeOf compiledIR := by\n change sizeOf elseIR + 6 ≤ sizeOf compiledIR\n simp_wf\n omega\n let branchExtraFuel :=\n sizeOf compiledIR - (sizeOf elseIR + 5) + wholeExtraFuel - 1\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n (fields := fields) (runtime := runtime)\n (state := state.setVar tempName condVal) (scope := scope)\n (inScopeNames := scope) (stmts := elseBranch)\n (extraFuel := branchExtraFuel)\n helse\n FunctionBody.scopeNamesIncluded_refl\n hscope hBindIte hbounded hRuntimeIte with\n ⟨elseIR', helseIR', helseSem⟩\n rw [helseIR] at helseIR'\n have helseEq : elseIR' = elseIR := (Except.ok.inj helseIR').symm\n rw [show elseIR' = elseIR from helseEq] at helseSem\n -- Fuel alignment: convert helseSem fuel to the form _ite_else expects\n have hfuelAlign : sizeOf elseIR + branchExtraFuel + 1 =\n sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf elseIR + 5) + wholeExtraFuel) := by\n simp only [List.append_nil, branchExtraFuel]\n have := hElse6\n omega\n have helseSem' :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime elseBranch)\n (execIRStmts (sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf elseIR + 5) + wholeExtraFuel))\n (state.setVar tempName condVal) elseIR) := by\n rw [← hfuelAlign]; exact helseSem\n -- Apply _ite_else to get match for the whole ITE statement list\n have hiteMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime\n [Stmt.ite cond thenBranch elseBranch])\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n state compiledIR) := by\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_else\n (fields := fields) (runtime := runtime) (state := state)\n (scope := scope) (cond := cond)\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n (extraFuel := wholeExtraFuel) (tempName := tempName)\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n (tailIR := []) (condValue := condVal)\n (sourceCondValue := condVal)\n helse helseSem' hCondSrc\n (by simp [hcondZero])\n hcondEval hcondZero rfl\n simp only [List.append_nil] at this\n exact this\n -- execStmt (.ite ...) = execStmtList elseBranch (by source semantics)\n have hexecStmtElse : SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch) =\n SourceSemantics.execStmtList fields runtime elseBranch := by\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n -- execStmtList [.ite ...] = execStmtList elseBranch (by terminal_ite_else_eq)\n have hsourceEq :=\n FunctionBody.execStmtList_terminal_core_ite_else_eq\n (fields := fields) (runtime := runtime) (scope := scope)\n (cond := cond) (thenBranch := thenBranch)\n (elseBranch := elseBranch) (rest := [])\n (condValue := condVal) helse hCondSrc\n (by simp [hcondZero])\n -- Rewrite hiteMatch source from execStmtList [.ite ...] to execStmtList elseBranch\n rw [hsourceEq] at hiteMatch\n -- Now hiteMatch : stmtResultMatchesIRExec fields\n -- (execStmtList fields runtime elseBranch) (execIRStmts ... state compiledIR)\n -- Convert to stmtResultMatchesIRExec about execStmt\n have hbodyMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch))\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n rw [hexecStmtElse, hwholeFuel]; exact hiteMatch\n refine ⟨_, _, rfl, rfl, ?_⟩\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n hbodyMatch\n (by rw [hexecStmtElse]\n exact FunctionBody.execStmtList_terminal_core_not_continue\n (fields := fields) (runtime := runtime) (scope := scope)\n (stmts := elseBranch) helse)\n · -- Condition is nonzero → take then branch\n have hBindIte :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n (scope := scope) (inScopeNames := scope)\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n have hRuntimeIte :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := tempName) (value := condVal) hruntime\n have hThen5 : sizeOf thenIR + 5 ≤ sizeOf compiledIR := by\n change sizeOf thenIR + 5 ≤ sizeOf compiledIR\n simp_wf\n omega\n let branchExtraFuel :=\n sizeOf compiledIR - (sizeOf thenIR + 5) + wholeExtraFuel\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n (fields := fields) (runtime := runtime)\n (state := state.setVar tempName condVal) (scope := scope)\n (inScopeNames := scope) (stmts := thenBranch)\n (extraFuel := branchExtraFuel)\n hthen\n FunctionBody.scopeNamesIncluded_refl\n hscope hBindIte hbounded hRuntimeIte with\n ⟨thenIR', hthenIR', hthenSem⟩\n rw [hthenIR] at hthenIR'\n have hthenEq : thenIR' = thenIR := (Except.ok.inj hthenIR').symm\n rw [show thenIR' = thenIR from hthenEq] at hthenSem\n -- Fuel alignment for then branch (has +1 on both sides, so direct)\n have hthenSem' :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime thenBranch)\n (execIRStmts (sizeOf thenIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf thenIR + 5) + wholeExtraFuel) + 1)\n (state.setVar tempName condVal) thenIR) := by\n simp only [List.append_nil, branchExtraFuel] at hthenSem ⊢\n exact hthenSem\n -- Apply _ite_then to get match for the whole ITE statement list\n have hiteMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime\n [Stmt.ite cond thenBranch elseBranch])\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n state compiledIR) := by\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_then\n (fields := fields) (runtime := runtime) (state := state)\n (scope := scope) (cond := cond)\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n (extraFuel := wholeExtraFuel) (tempName := tempName)\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n (tailIR := []) (condValue := condVal)\n (sourceCondValue := condVal)\n hthen hthenSem' hCondSrc\n (by simp [hcondZero])\n hcondEval\n (by intro hzero; exact hcondZero hzero) rfl\n simp only [List.append_nil] at this\n exact this\n -- execStmt (.ite ...) = execStmtList thenBranch (by source semantics)\n have hexecStmtThen : SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch) =\n SourceSemantics.execStmtList fields runtime thenBranch := by\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n -- execStmtList [.ite ...] = execStmtList thenBranch\n have hsourceEq :=\n FunctionBody.execStmtList_terminal_core_ite_then_eq\n (fields := fields) (runtime := runtime) (scope := scope)\n (cond := cond) (thenBranch := thenBranch)\n (elseBranch := elseBranch) (rest := [])\n (condValue := condVal) hthen hCondSrc\n (by simp [hcondZero])\n rw [hsourceEq] at hiteMatch\n have hbodyMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch))\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n rw [hexecStmtThen, hwholeFuel]; exact hiteMatch\n refine ⟨_, _, rfl, rfl, ?_⟩\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n hbodyMatch\n (by rw [hexecStmtThen]\n exact FunctionBody.execStmtList_terminal_core_not_continue\n (fields := fields) (runtime := runtime) (scope := scope)\n (stmts := thenBranch) hthen)","n_chars":12831,"n_subproofs":32,"n_tactics":230,"cyclomatic":8,"n_automation":29,"n_rewrites":20,"n_structural":25,"automation_only":false,"max_nesting":18}],"string":"[\n {\n \"theorem_name\": \"compiledStmtStep_mstore_single\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 7,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\\n hoffsetIRInternal, hvalueIRInternal, Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_mstore_single_preserves\\n hcoreOffset hinScopeOffset hcoreValue hinScopeValue hoffsetIR hvalueIR\",\n \"n_chars\": 440,\n \"n_subproofs\": 2,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_tstore_single\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 7,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\\n hoffsetIRInternal, hvalueIRInternal, Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_tstore_single_preserves\\n hcoreOffset hinScopeOffset hcoreValue hinScopeValue hoffsetIR hvalueIR\",\n \"n_chars\": 440,\n \"n_subproofs\": 2,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingUint_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 729,\n \"n_subproofs\": 2,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compileExprList_core_ok\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 19,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction exprs with\\n | nil =>\\n exact ⟨[], by\\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\\n pure, Except.pure]⟩\\n | cons expr rest ih =>\\n have hhead : FunctionBody.ExprCompileCore expr := hcore expr (by simp)\\n have htail : ∀ e ∈ rest, FunctionBody.ExprCompileCore e := by\\n intro e he\\n exact hcore e (by simp [he])\\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hhead with ⟨exprIR, hexprIR⟩\\n rcases ih htail with ⟨restIR, hrestIR⟩\\n have hexprIRInternal := compileExprWithInternals_nil_ok hexprIR\\n have hrestIRInternal := compileExprListWithInternals_nil_ok hrestIR\\n exact ⟨exprIR :: restIR, by\\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\\n hexprIRInternal, hrestIRInternal, bind, Except.bind, pure, Except.pure]\\n ⟩\",\n \"n_chars\": 930,\n \"n_subproofs\": 4,\n \"n_tactics\": 19,\n \"cyclomatic\": 4,\n \"n_automation\": 4,\n \"n_rewrites\": 0,\n \"n_structural\": 7,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"eval_compileExprList_core_of_scope\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction exprs generalizing exprIRs with\\n | nil =>\\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals] at hcompiled\\n cases hcompiled\\n exact ⟨[], rfl, .nil⟩\\n | cons expr rest ih =>\\n have hhead : FunctionBody.ExprCompileCore expr := hcore expr (by simp)\\n have htail :\\n ∀ expr' ∈ rest, FunctionBody.ExprCompileCore expr' := by\\n intro expr' hexpr'\\n exact hcore expr' (by simp [hexpr'])\\n have htailScope :\\n ∀ expr' ∈ rest, FunctionBody.exprBoundNamesInScope expr' scope := by\\n intro expr' hexpr'\\n exact hinScope expr' (by simp [hexpr'])\\n rcases compileExprList_core_ok (fields := fields) htail with ⟨restIRs, hrestIRs⟩\\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hhead with ⟨exprIR, hexprIR⟩\\n have hexprIRInternal := compileExprWithInternals_nil_ok hexprIR\\n have hrestIRsInternal := compileExprListWithInternals_nil_ok hrestIRs\\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\\n hexprIRInternal, hrestIRsInternal] at hcompiled\\n injection hcompiled with hcompiledTail\\n subst hcompiledTail\\n rcases eval_compileExpr_core_some_of_scope\\n (expr := expr) (exprIR := exprIR) hhead hexact (hinScope expr (by simp))\\n hbounded hscope hruntime hexprIR with\\n ⟨headVal, hheadVal, hheadEval⟩\\n rcases ih htail htailScope hrestIRs with\\n ⟨restVals, hrestVals, hrestEval⟩\\n refine ⟨headVal :: restVals, ?_, ?_⟩\\n · simp [SourceSemantics.evalExprList, hheadVal, hrestVals]\\n · exact .cons hheadEval hrestEval\",\n \"n_chars\": 1688,\n \"n_subproofs\": 5,\n \"n_tactics\": 33,\n \"cyclomatic\": 7,\n \"n_automation\": 8,\n \"n_rewrites\": 1,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingChain_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRsInternal := compileExprListWithInternals_nil_ok hkeyIRs\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMappingChain,\\n hmapping, hwriteSlots, hkeyIRsInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMappingChain_singleSlot_of_slotSafety_preserves\\n hcoreKeys hinScopeKeys hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIRs hvalueIR\",\n \"n_chars\": 739,\n \"n_subproofs\": 2,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMapping_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 725,\n \"n_subproofs\": 2,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingWord_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMappingWord_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 729,\n \"n_subproofs\": 2,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 14,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingPackedSlotWrite,\\n hmapping, hpacked, hwriteSlots, hkeyIRInternal, hvalueIRInternal, Bool.not_true, bne_self_eq_false,\\n ite_false, ite_true, pure, Except.pure, bind, Except.bind]\\n simp [hfind, fieldLoadBuiltin, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue\\n hcompatValue hcompatPacked hcompatSlotWord hcompatSlotCleared\\n hpacked hwriteSlots hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 945,\n \"n_subproofs\": 2,\n \"n_tactics\": 14,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setStructMember_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 13,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember,\\n CompilationModel.compileMappingSlotWrite, hmapping, hnotMapping2, hmembers, hmember,\\n hwriteSlots, hkeyIRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setStructMember_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue hmembers hmember hwriteSlots\\n hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 831,\n \"n_subproofs\": 2,\n \"n_tactics\": 13,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping2_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 13,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMapping2,\\n hmapping2, hwriteSlots, hkey1IRInternal, hkey2IRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMapping2_singleSlot_of_slotSafety_preserves\\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\",\n \"n_chars\": 848,\n \"n_subproofs\": 3,\n \"n_tactics\": 13,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 13,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMapping2Word,\\n hmapping2, hwriteSlots, hkey1IRInternal, hkey2IRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\",\n \"n_chars\": 856,\n \"n_subproofs\": 3,\n \"n_tactics\": 13,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setStructMember2_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 14,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember2,\\n hmapping2, hmembers, hmember, hwriteSlots, hkey1IRInternal, hkey2IRInternal,\\n hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\\n hmembers hmember hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\",\n \"n_chars\": 900,\n \"n_subproofs\": 3,\n \"n_tactics\": 14,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_ite\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 237,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcond with ⟨condIR, hcondIR⟩\\n rcases FunctionBody.compileStmtList_terminal_core_ok\\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := thenBranch)\\n hthen with ⟨thenIR, hthenIR⟩\\n rcases FunctionBody.compileStmtList_terminal_core_ok\\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := elseBranch)\\n helse with ⟨elseIR, helseIR⟩\\n have helseNonempty : elseBranch.isEmpty = false := by\\n cases elseBranch with\\n | nil => exfalso; exact FunctionBody.stmtListTerminalCore_ne_nil helse rfl\\n | cons => simp\\n let tempName :=\\n CompilationModel.pickFreshName \\\"__ite_cond\\\"\\n (scope ++ collectExprNames cond ++\\n collectStmtListNames thenBranch ++ collectStmtListNames elseBranch)\\n let compiledIR :=\\n [YulStmt.block\\n [ YulStmt.let_ tempName condIR\\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\\n , YulStmt.if_ (YulExpr.call \\\"iszero\\\" [YulExpr.ident tempName]) elseIR ]]\\n refine ⟨compiledIR, ?_⟩\\n refine\\n { compileOk := ?_\\n preserves := ?_ }\\n · show CompilationModel.compileStmt fields [] [] .calldata [] false scope []\\n (.ite cond thenBranch elseBranch) = Except.ok compiledIR\\n have hcondIRInternal := compileExprWithInternals_nil_ok hcondIR\\n unfold CompilationModel.compileStmt CompilationModel.compileStmtWithFork\\n simp [FunctionBody.compileStmtListWithFork_cancun_eq_compileStmtList,\\n hcondIRInternal, hthenIR, helseIR, Except.bind, helseNonempty]\\n simp [compiledIR, tempName, List.append_assoc, Bind.bind, Except.bind,\\n Pure.pure, Except.pure]\\n · intro runtime state extraFuel hexact hscope hbounded hruntime hslack\\n set wholeExtraFuel := extraFuel - (sizeOf compiledIR - compiledIR.length) with hWF\\n have hsizeOf_eq : sizeOf compiledIR = 1 + sizeOf (YulStmt.block\\n [ YulStmt.let_ tempName condIR\\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\\n , YulStmt.if_ (YulExpr.call \\\"iszero\\\" [YulExpr.ident tempName]) elseIR ]) + 1 := by\\n rfl\\n have hlength_eq : compiledIR.length = 1 := by rfl\\n have hwholeFuel :\\n compiledIR.length + extraFuel + 1 =\\n sizeOf compiledIR + wholeExtraFuel + 1 := by\\n rw [hWF, hsizeOf_eq, hlength_eq]\\n have : sizeOf compiledIR - compiledIR.length ≤ extraFuel := hslack\\n rw [hsizeOf_eq, hlength_eq] at this\\n omega\\n have hpresent : FunctionBody.exprBoundNamesPresent cond runtime.bindings :=\\n FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope\\n -- Extract the Nat condition value via the eval bridge\\n have heval := FunctionBody.eval_compileExpr_core_of_scope\\n hcond hexact hinScope hbounded hpresent hruntime\\n rw [hcondIR] at heval; simp [Except.toOption] at heval\\n rcases hCondIRVal : evalIRExpr state condIR with _ | condVal\\n · simp [hCondIRVal, Option.bind] at heval\\n · simp [hCondIRVal, Option.bind] at heval\\n have hCondSrc : SourceSemantics.evalExpr fields runtime cond = some condVal :=\\n heval.symm\\n have hcondEval : evalIRExpr state condIR = some condVal := hCondIRVal\\n by_cases hcondZero : condVal = 0\\n · -- Condition is zero → take else branch\\n have hBindIte :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\\n (scope := scope) (inScopeNames := scope)\\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\\n have hRuntimeIte :=\\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\\n (name := tempName) (value := condVal) hruntime\\n have hElse6 : sizeOf elseIR + 6 ≤ sizeOf compiledIR := by\\n change sizeOf elseIR + 6 ≤ sizeOf compiledIR\\n simp_wf\\n omega\\n let branchExtraFuel :=\\n sizeOf compiledIR - (sizeOf elseIR + 5) + wholeExtraFuel - 1\\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\\n (fields := fields) (runtime := runtime)\\n (state := state.setVar tempName condVal) (scope := scope)\\n (inScopeNames := scope) (stmts := elseBranch)\\n (extraFuel := branchExtraFuel)\\n helse\\n FunctionBody.scopeNamesIncluded_refl\\n hscope hBindIte hbounded hRuntimeIte with\\n ⟨elseIR', helseIR', helseSem⟩\\n rw [helseIR] at helseIR'\\n have helseEq : elseIR' = elseIR := (Except.ok.inj helseIR').symm\\n rw [show elseIR' = elseIR from helseEq] at helseSem\\n -- Fuel alignment: convert helseSem fuel to the form _ite_else expects\\n have hfuelAlign : sizeOf elseIR + branchExtraFuel + 1 =\\n sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\\n (sizeOf elseIR + 5) + wholeExtraFuel) := by\\n simp only [List.append_nil, branchExtraFuel]\\n have := hElse6\\n omega\\n have helseSem' :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmtList fields runtime elseBranch)\\n (execIRStmts (sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\\n (sizeOf elseIR + 5) + wholeExtraFuel))\\n (state.setVar tempName condVal) elseIR) := by\\n rw [← hfuelAlign]; exact helseSem\\n -- Apply _ite_else to get match for the whole ITE statement list\\n have hiteMatch :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmtList fields runtime\\n [Stmt.ite cond thenBranch elseBranch])\\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\\n state compiledIR) := by\\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_else\\n (fields := fields) (runtime := runtime) (state := state)\\n (scope := scope) (cond := cond)\\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\\n (extraFuel := wholeExtraFuel) (tempName := tempName)\\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\\n (tailIR := []) (condValue := condVal)\\n (sourceCondValue := condVal)\\n helse helseSem' hCondSrc\\n (by simp [hcondZero])\\n hcondEval hcondZero rfl\\n simp only [List.append_nil] at this\\n exact this\\n -- execStmt (.ite ...) = execStmtList elseBranch (by source semantics)\\n have hexecStmtElse : SourceSemantics.execStmt fields runtime\\n (Stmt.ite cond thenBranch elseBranch) =\\n SourceSemantics.execStmtList fields runtime elseBranch := by\\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\\n -- execStmtList [.ite ...] = execStmtList elseBranch (by terminal_ite_else_eq)\\n have hsourceEq :=\\n FunctionBody.execStmtList_terminal_core_ite_else_eq\\n (fields := fields) (runtime := runtime) (scope := scope)\\n (cond := cond) (thenBranch := thenBranch)\\n (elseBranch := elseBranch) (rest := [])\\n (condValue := condVal) helse hCondSrc\\n (by simp [hcondZero])\\n -- Rewrite hiteMatch source from execStmtList [.ite ...] to execStmtList elseBranch\\n rw [hsourceEq] at hiteMatch\\n -- Now hiteMatch : stmtResultMatchesIRExec fields\\n -- (execStmtList fields runtime elseBranch) (execIRStmts ... state compiledIR)\\n -- Convert to stmtResultMatchesIRExec about execStmt\\n have hbodyMatch :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmt fields runtime\\n (Stmt.ite cond thenBranch elseBranch))\\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\\n rw [hexecStmtElse, hwholeFuel]; exact hiteMatch\\n refine ⟨_, _, rfl, rfl, ?_⟩\\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\\n hbodyMatch\\n (by rw [hexecStmtElse]\\n exact FunctionBody.execStmtList_terminal_core_not_continue\\n (fields := fields) (runtime := runtime) (scope := scope)\\n (stmts := elseBranch) helse)\\n · -- Condition is nonzero → take then branch\\n have hBindIte :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\\n (scope := scope) (inScopeNames := scope)\\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\\n have hRuntimeIte :=\\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\\n (name := tempName) (value := condVal) hruntime\\n have hThen5 : sizeOf thenIR + 5 ≤ sizeOf compiledIR := by\\n change sizeOf thenIR + 5 ≤ sizeOf compiledIR\\n simp_wf\\n omega\\n let branchExtraFuel :=\\n sizeOf compiledIR - (sizeOf thenIR + 5) + wholeExtraFuel\\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\\n (fields := fields) (runtime := runtime)\\n (state := state.setVar tempName condVal) (scope := scope)\\n (inScopeNames := scope) (stmts := thenBranch)\\n (extraFuel := branchExtraFuel)\\n hthen\\n FunctionBody.scopeNamesIncluded_refl\\n hscope hBindIte hbounded hRuntimeIte with\\n ⟨thenIR', hthenIR', hthenSem⟩\\n rw [hthenIR] at hthenIR'\\n have hthenEq : thenIR' = thenIR := (Except.ok.inj hthenIR').symm\\n rw [show thenIR' = thenIR from hthenEq] at hthenSem\\n -- Fuel alignment for then branch (has +1 on both sides, so direct)\\n have hthenSem' :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmtList fields runtime thenBranch)\\n (execIRStmts (sizeOf thenIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\\n (sizeOf thenIR + 5) + wholeExtraFuel) + 1)\\n (state.setVar tempName condVal) thenIR) := by\\n simp only [List.append_nil, branchExtraFuel] at hthenSem ⊢\\n exact hthenSem\\n -- Apply _ite_then to get match for the whole ITE statement list\\n have hiteMatch :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmtList fields runtime\\n [Stmt.ite cond thenBranch elseBranch])\\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\\n state compiledIR) := by\\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_then\\n (fields := fields) (runtime := runtime) (state := state)\\n (scope := scope) (cond := cond)\\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\\n (extraFuel := wholeExtraFuel) (tempName := tempName)\\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\\n (tailIR := []) (condValue := condVal)\\n (sourceCondValue := condVal)\\n hthen hthenSem' hCondSrc\\n (by simp [hcondZero])\\n hcondEval\\n (by intro hzero; exact hcondZero hzero) rfl\\n simp only [List.append_nil] at this\\n exact this\\n -- execStmt (.ite ...) = execStmtList thenBranch (by source semantics)\\n have hexecStmtThen : SourceSemantics.execStmt fields runtime\\n (Stmt.ite cond thenBranch elseBranch) =\\n SourceSemantics.execStmtList fields runtime thenBranch := by\\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\\n -- execStmtList [.ite ...] = execStmtList thenBranch\\n have hsourceEq :=\\n FunctionBody.execStmtList_terminal_core_ite_then_eq\\n (fields := fields) (runtime := runtime) (scope := scope)\\n (cond := cond) (thenBranch := thenBranch)\\n (elseBranch := elseBranch) (rest := [])\\n (condValue := condVal) hthen hCondSrc\\n (by simp [hcondZero])\\n rw [hsourceEq] at hiteMatch\\n have hbodyMatch :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmt fields runtime\\n (Stmt.ite cond thenBranch elseBranch))\\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\\n rw [hexecStmtThen, hwholeFuel]; exact hiteMatch\\n refine ⟨_, _, rfl, rfl, ?_⟩\\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\\n hbodyMatch\\n (by rw [hexecStmtThen]\\n exact FunctionBody.execStmtList_terminal_core_not_continue\\n (fields := fields) (runtime := runtime) (scope := scope)\\n (stmts := thenBranch) hthen)\",\n \"n_chars\": 12831,\n \"n_subproofs\": 32,\n \"n_tactics\": 230,\n \"cyclomatic\": 8,\n \"n_automation\": 29,\n \"n_rewrites\": 20,\n \"n_structural\": 25,\n \"automation_only\": false,\n \"max_nesting\": 18\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compileExprWithInternals_nil_ok","text":"private theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\n simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\n\n","fan_in":14,"n_lines":7,"n_chars":397,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":true,"max_nesting":2}],"string":"[\n {\n \"name\": \"compileExprWithInternals_nil_ok\",\n \"text\": \"private theorem compileExprWithInternals_nil_ok\\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\\n CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\\n simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\\n\\n\",\n \"fan_in\": 14,\n \"n_lines\": 7,\n \"n_chars\": 397,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": true,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_ite","fan_in":1,"n_deps_direct":2,"n_deps_transitive":2,"n_lines":248,"n_chars":13312,"n_subproofs":32,"n_tactics":230,"cyclomatic":8,"n_automation":29,"n_rewrites":20,"n_structural":25,"automation_only":false,"max_nesting":18}],"string":"[\n {\n \"name\": \"compiledStmtStep_ite\",\n \"fan_in\": 1,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 2,\n \"n_lines\": 248,\n \"n_chars\": 13312,\n \"n_subproofs\": 32,\n \"n_tactics\": 230,\n \"cyclomatic\": 8,\n \"n_automation\": 29,\n \"n_rewrites\": 20,\n \"n_structural\": 25,\n \"automation_only\": false,\n \"max_nesting\": 18\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n {fields : List Field}\n {scope : List String}\n {sourceResult : SourceSemantics.StmtResult}\n {irExec : IRExecResult}\n (hmatch : FunctionBody.stmtResultMatchesIRExec fields sourceResult irExec)\n (hnotContinue : ∀ next, sourceResult ≠ .continue next) :\n stmtStepMatchesIRExec fields scope sourceResult irExec := by\n cases sourceResult <;> cases irExec <;>\n simp [stmtStepMatchesIRExec, FunctionBody.stmtResultMatchesIRExec] at hmatch ⊢\n · exact False.elim (hnotContinue _ rfl)\n · exact hmatch\n · exact hmatch\n\ntheorem compiledStmtStep_ite\n {fields : List Field}\n {scope : List String}\n {cond : Expr}\n {thenBranch elseBranch : List Stmt}\n (hcond : FunctionBody.ExprCompileCore cond)\n (hinScope : FunctionBody.exprBoundNamesInScope cond scope)\n (hthen : FunctionBody.StmtListTerminalCore scope thenBranch)\n (helse : FunctionBody.StmtListTerminalCore scope elseBranch) :\n ∃ compiledIR, CompiledStmtStep fields scope (.ite cond thenBranch elseBranch) compiledIR := sorry\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\n simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n {fields : List Field}\n {scope : List String}\n {sourceResult : SourceSemantics.StmtResult}\n {irExec : IRExecResult}\n (hmatch : FunctionBody.stmtResultMatchesIRExec fields sourceResult irExec)\n (hnotContinue : ∀ next, sourceResult ≠ .continue next) :\n stmtStepMatchesIRExec fields scope sourceResult irExec := by\n cases sourceResult <;> cases irExec <;>\n simp [stmtStepMatchesIRExec, FunctionBody.stmtResultMatchesIRExec] at hmatch ⊢\n · exact False.elim (hnotContinue _ rfl)\n · exact hmatch\n · exact hmatch\n\ntheorem compiledStmtStep_ite\n {fields : List Field}\n {scope : List String}\n {cond : Expr}\n {thenBranch elseBranch : List Stmt}\n (hcond : FunctionBody.ExprCompileCore cond)\n (hinScope : FunctionBody.exprBoundNamesInScope cond scope)\n (hthen : FunctionBody.StmtListTerminalCore scope thenBranch)\n (helse : FunctionBody.StmtListTerminalCore scope elseBranch) :\n ∃ compiledIR, CompiledStmtStep fields scope (.ite cond thenBranch elseBranch) compiledIR := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcond with ⟨condIR, hcondIR⟩\n rcases FunctionBody.compileStmtList_terminal_core_ok\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := thenBranch)\n hthen with ⟨thenIR, hthenIR⟩\n rcases FunctionBody.compileStmtList_terminal_core_ok\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := elseBranch)\n helse with ⟨elseIR, helseIR⟩\n have helseNonempty : elseBranch.isEmpty = false := by\n cases elseBranch with\n | nil => exfalso; exact FunctionBody.stmtListTerminalCore_ne_nil helse rfl\n | cons => simp\n let tempName :=\n CompilationModel.pickFreshName \"__ite_cond\"\n (scope ++ collectExprNames cond ++\n collectStmtListNames thenBranch ++ collectStmtListNames elseBranch)\n let compiledIR :=\n [YulStmt.block\n [ YulStmt.let_ tempName condIR\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\n , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]]\n refine ⟨compiledIR, ?_⟩\n refine\n { compileOk := ?_\n preserves := ?_ }\n · show CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (.ite cond thenBranch elseBranch) = Except.ok compiledIR\n have hcondIRInternal := compileExprWithInternals_nil_ok hcondIR\n unfold CompilationModel.compileStmt CompilationModel.compileStmtWithFork\n simp [FunctionBody.compileStmtListWithFork_cancun_eq_compileStmtList,\n hcondIRInternal, hthenIR, helseIR, Except.bind, helseNonempty]\n simp [compiledIR, tempName, List.append_assoc, Bind.bind, Except.bind,\n Pure.pure, Except.pure]\n · intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n set wholeExtraFuel := extraFuel - (sizeOf compiledIR - compiledIR.length) with hWF\n have hsizeOf_eq : sizeOf compiledIR = 1 + sizeOf (YulStmt.block\n [ YulStmt.let_ tempName condIR\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\n , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]) + 1 := by\n rfl\n have hlength_eq : compiledIR.length = 1 := by rfl\n have hwholeFuel :\n compiledIR.length + extraFuel + 1 =\n sizeOf compiledIR + wholeExtraFuel + 1 := by\n rw [hWF, hsizeOf_eq, hlength_eq]\n have : sizeOf compiledIR - compiledIR.length ≤ extraFuel := hslack\n rw [hsizeOf_eq, hlength_eq] at this\n omega\n have hpresent : FunctionBody.exprBoundNamesPresent cond runtime.bindings :=\n FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope\n -- Extract the Nat condition value via the eval bridge\n have heval := FunctionBody.eval_compileExpr_core_of_scope\n hcond hexact hinScope hbounded hpresent hruntime\n rw [hcondIR] at heval; simp [Except.toOption] at heval\n rcases hCondIRVal : evalIRExpr state condIR with _ | condVal\n · simp [hCondIRVal, Option.bind] at heval\n · simp [hCondIRVal, Option.bind] at heval\n have hCondSrc : SourceSemantics.evalExpr fields runtime cond = some condVal :=\n heval.symm\n have hcondEval : evalIRExpr state condIR = some condVal := hCondIRVal\n by_cases hcondZero : condVal = 0\n · -- Condition is zero → take else branch\n have hBindIte :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n (scope := scope) (inScopeNames := scope)\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n have hRuntimeIte :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := tempName) (value := condVal) hruntime\n have hElse6 : sizeOf elseIR + 6 ≤ sizeOf compiledIR := by\n change sizeOf elseIR + 6 ≤ sizeOf compiledIR\n simp_wf\n omega\n let branchExtraFuel :=\n sizeOf compiledIR - (sizeOf elseIR + 5) + wholeExtraFuel - 1\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n (fields := fields) (runtime := runtime)\n (state := state.setVar tempName condVal) (scope := scope)\n (inScopeNames := scope) (stmts := elseBranch)\n (extraFuel := branchExtraFuel)\n helse\n FunctionBody.scopeNamesIncluded_refl\n hscope hBindIte hbounded hRuntimeIte with\n ⟨elseIR', helseIR', helseSem⟩\n rw [helseIR] at helseIR'\n have helseEq : elseIR' = elseIR := (Except.ok.inj helseIR').symm\n rw [show elseIR' = elseIR from helseEq] at helseSem\n -- Fuel alignment: convert helseSem fuel to the form _ite_else expects\n have hfuelAlign : sizeOf elseIR + branchExtraFuel + 1 =\n sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf elseIR + 5) + wholeExtraFuel) := by\n simp only [List.append_nil, branchExtraFuel]\n have := hElse6\n omega\n have helseSem' :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime elseBranch)\n (execIRStmts (sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf elseIR + 5) + wholeExtraFuel))\n (state.setVar tempName condVal) elseIR) := by\n rw [← hfuelAlign]; exact helseSem\n -- Apply _ite_else to get match for the whole ITE statement list\n have hiteMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime\n [Stmt.ite cond thenBranch elseBranch])\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n state compiledIR) := by\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_else\n (fields := fields) (runtime := runtime) (state := state)\n (scope := scope) (cond := cond)\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n (extraFuel := wholeExtraFuel) (tempName := tempName)\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n (tailIR := []) (condValue := condVal)\n (sourceCondValue := condVal)\n helse helseSem' hCondSrc\n (by simp [hcondZero])\n hcondEval hcondZero rfl\n simp only [List.append_nil] at this\n exact this\n -- execStmt (.ite ...) = execStmtList elseBranch (by source semantics)\n have hexecStmtElse : SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch) =\n SourceSemantics.execStmtList fields runtime elseBranch := by\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n -- execStmtList [.ite ...] = execStmtList elseBranch (by terminal_ite_else_eq)\n have hsourceEq :=\n FunctionBody.execStmtList_terminal_core_ite_else_eq\n (fields := fields) (runtime := runtime) (scope := scope)\n (cond := cond) (thenBranch := thenBranch)\n (elseBranch := elseBranch) (rest := [])\n (condValue := condVal) helse hCondSrc\n (by simp [hcondZero])\n -- Rewrite hiteMatch source from execStmtList [.ite ...] to execStmtList elseBranch\n rw [hsourceEq] at hiteMatch\n -- Now hiteMatch : stmtResultMatchesIRExec fields\n -- (execStmtList fields runtime elseBranch) (execIRStmts ... state compiledIR)\n -- Convert to stmtResultMatchesIRExec about execStmt\n have hbodyMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch))\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n rw [hexecStmtElse, hwholeFuel]; exact hiteMatch\n refine ⟨_, _, rfl, rfl, ?_⟩\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n hbodyMatch\n (by rw [hexecStmtElse]\n exact FunctionBody.execStmtList_terminal_core_not_continue\n (fields := fields) (runtime := runtime) (scope := scope)\n (stmts := elseBranch) helse)\n · -- Condition is nonzero → take then branch\n have hBindIte :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n (scope := scope) (inScopeNames := scope)\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n have hRuntimeIte :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := tempName) (value := condVal) hruntime\n have hThen5 : sizeOf thenIR + 5 ≤ sizeOf compiledIR := by\n change sizeOf thenIR + 5 ≤ sizeOf compiledIR\n simp_wf\n omega\n let branchExtraFuel :=\n sizeOf compiledIR - (sizeOf thenIR + 5) + wholeExtraFuel\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n (fields := fields) (runtime := runtime)\n (state := state.setVar tempName condVal) (scope := scope)\n (inScopeNames := scope) (stmts := thenBranch)\n (extraFuel := branchExtraFuel)\n hthen\n FunctionBody.scopeNamesIncluded_refl\n hscope hBindIte hbounded hRuntimeIte with\n ⟨thenIR', hthenIR', hthenSem⟩\n rw [hthenIR] at hthenIR'\n have hthenEq : thenIR' = thenIR := (Except.ok.inj hthenIR').symm\n rw [show thenIR' = thenIR from hthenEq] at hthenSem\n -- Fuel alignment for then branch (has +1 on both sides, so direct)\n have hthenSem' :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime thenBranch)\n (execIRStmts (sizeOf thenIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf thenIR + 5) + wholeExtraFuel) + 1)\n (state.setVar tempName condVal) thenIR) := by\n simp only [List.append_nil, branchExtraFuel] at hthenSem ⊢\n exact hthenSem\n -- Apply _ite_then to get match for the whole ITE statement list\n have hiteMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime\n [Stmt.ite cond thenBranch elseBranch])\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n state compiledIR) := by\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_then\n (fields := fields) (runtime := runtime) (state := state)\n (scope := scope) (cond := cond)\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n (extraFuel := wholeExtraFuel) (tempName := tempName)\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n (tailIR := []) (condValue := condVal)\n (sourceCondValue := condVal)\n hthen hthenSem' hCondSrc\n (by simp [hcondZero])\n hcondEval\n (by intro hzero; exact hcondZero hzero) rfl\n simp only [List.append_nil] at this\n exact this\n -- execStmt (.ite ...) = execStmtList thenBranch (by source semantics)\n have hexecStmtThen : SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch) =\n SourceSemantics.execStmtList fields runtime thenBranch := by\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n -- execStmtList [.ite ...] = execStmtList thenBranch\n have hsourceEq :=\n FunctionBody.execStmtList_terminal_core_ite_then_eq\n (fields := fields) (runtime := runtime) (scope := scope)\n (cond := cond) (thenBranch := thenBranch)\n (elseBranch := elseBranch) (rest := [])\n (condValue := condVal) hthen hCondSrc\n (by simp [hcondZero])\n rw [hsourceEq] at hiteMatch\n have hbodyMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch))\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n rw [hexecStmtThen, hwholeFuel]; exact hiteMatch\n refine ⟨_, _, rfl, rfl, ?_⟩\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n hbodyMatch\n (by rw [hexecStmtThen]\n exact FunctionBody.execStmtList_terminal_core_not_continue\n (fields := fields) (runtime := runtime) (scope := scope)\n (stmts := thenBranch) hthen)\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -12,6 +12,12 @@\n \n attribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n \n+private theorem compileExprWithInternals_nil_ok\n+ {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n+ (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n+ CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\n+ simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\n+\n set_option maxHeartbeats 800000 in\n private theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n@@ -1948,7 +1954,243 @@\n (hinScope : FunctionBody.exprBoundNamesInScope cond scope)\n (hthen : FunctionBody.StmtListTerminalCore scope thenBranch)\n (helse : FunctionBody.StmtListTerminalCore scope elseBranch) :\n- ∃ compiledIR, CompiledStmtStep fields scope (.ite cond thenBranch elseBranch) compiledIR := sorry\n+ ∃ compiledIR, CompiledStmtStep fields scope (.ite cond thenBranch elseBranch) compiledIR := by\n+ rcases FunctionBody.compileExpr_core_ok (fields := fields) hcond with ⟨condIR, hcondIR⟩\n+ rcases FunctionBody.compileStmtList_terminal_core_ok\n+ (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := thenBranch)\n+ hthen with ⟨thenIR, hthenIR⟩\n+ rcases FunctionBody.compileStmtList_terminal_core_ok\n+ (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := elseBranch)\n+ helse with ⟨elseIR, helseIR⟩\n+ have helseNonempty : elseBranch.isEmpty = false := by\n+ cases elseBranch with\n+ | nil => exfalso; exact FunctionBody.stmtListTerminalCore_ne_nil helse rfl\n+ | cons => simp\n+ let tempName :=\n+ CompilationModel.pickFreshName \"__ite_cond\"\n+ (scope ++ collectExprNames cond ++\n+ collectStmtListNames thenBranch ++ collectStmtListNames elseBranch)\n+ let compiledIR :=\n+ [YulStmt.block\n+ [ YulStmt.let_ tempName condIR\n+ , YulStmt.if_ (YulExpr.ident tempName) thenIR\n+ , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]]\n+ refine ⟨compiledIR, ?_⟩\n+ refine\n+ { compileOk := ?_\n+ preserves := ?_ }\n+ · show CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n+ (.ite cond thenBranch elseBranch) = Except.ok compiledIR\n+ have hcondIRInternal := compileExprWithInternals_nil_ok hcondIR\n+ unfold CompilationModel.compileStmt CompilationModel.compileStmtWithFork\n+ simp [FunctionBody.compileStmtListWithFork_cancun_eq_compileStmtList,\n+ hcondIRInternal, hthenIR, helseIR, Except.bind, helseNonempty]\n+ simp [compiledIR, tempName, List.append_assoc, Bind.bind, Except.bind,\n+ Pure.pure, Except.pure]\n+ · intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n+ set wholeExtraFuel := extraFuel - (sizeOf compiledIR - compiledIR.length) with hWF\n+ have hsizeOf_eq : sizeOf compiledIR = 1 + sizeOf (YulStmt.block\n+ [ YulStmt.let_ tempName condIR\n+ , YulStmt.if_ (YulExpr.ident tempName) thenIR\n+ , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]) + 1 := by\n+ rfl\n+ have hlength_eq : compiledIR.length = 1 := by rfl\n+ have hwholeFuel :\n+ compiledIR.length + extraFuel + 1 =\n+ sizeOf compiledIR + wholeExtraFuel + 1 := by\n+ rw [hWF, hsizeOf_eq, hlength_eq]\n+ have : sizeOf compiledIR - compiledIR.length ≤ extraFuel := hslack\n+ rw [hsizeOf_eq, hlength_eq] at this\n+ omega\n+ have hpresent : FunctionBody.exprBoundNamesPresent cond runtime.bindings :=\n+ FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope\n+ -- Extract the Nat condition value via the eval bridge\n+ have heval := FunctionBody.eval_compileExpr_core_of_scope\n+ hcond hexact hinScope hbounded hpresent hruntime\n+ rw [hcondIR] at heval; simp [Except.toOption] at heval\n+ rcases hCondIRVal : evalIRExpr state condIR with _ | condVal\n+ · simp [hCondIRVal, Option.bind] at heval\n+ · simp [hCondIRVal, Option.bind] at heval\n+ have hCondSrc : SourceSemantics.evalExpr fields runtime cond = some condVal :=\n+ heval.symm\n+ have hcondEval : evalIRExpr state condIR = some condVal := hCondIRVal\n+ by_cases hcondZero : condVal = 0\n+ · -- Condition is zero → take else branch\n+ have hBindIte :=\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n+ (scope := scope) (inScopeNames := scope)\n+ (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n+ (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n+ have hRuntimeIte :=\n+ FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n+ (name := tempName) (value := condVal) hruntime\n+ have hElse6 : sizeOf elseIR + 6 ≤ sizeOf compiledIR := by\n+ change sizeOf elseIR + 6 ≤ sizeOf compiledIR\n+ simp_wf\n+ omega\n+ let branchExtraFuel :=\n+ sizeOf compiledIR - (sizeOf elseIR + 5) + wholeExtraFuel - 1\n+ rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n+ (fields := fields) (runtime := runtime)\n+ (state := state.setVar tempName condVal) (scope := scope)\n+ (inScopeNames := scope) (stmts := elseBranch)\n+ (extraFuel := branchExtraFuel)\n+ helse\n+ FunctionBody.scopeNamesIncluded_refl\n+ hscope hBindIte hbounded hRuntimeIte with\n+ ⟨elseIR', helseIR', helseSem⟩\n+ rw [helseIR] at helseIR'\n+ have helseEq : elseIR' = elseIR := (Except.ok.inj helseIR').symm\n+ rw [show elseIR' = elseIR from helseEq] at helseSem\n+ -- Fuel alignment: convert helseSem fuel to the form _ite_else expects\n+ have hfuelAlign : sizeOf elseIR + branchExtraFuel + 1 =\n+ sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n+ (sizeOf elseIR + 5) + wholeExtraFuel) := by\n+ simp only [List.append_nil, branchExtraFuel]\n+ have := hElse6\n+ omega\n+ have helseSem' :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmtList fields runtime elseBranch)\n+ (execIRStmts (sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n+ (sizeOf elseIR + 5) + wholeExtraFuel))\n+ (state.setVar tempName condVal) elseIR) := by\n+ rw [← hfuelAlign]; exact helseSem\n+ -- Apply _ite_else to get match for the whole ITE statement list\n+ have hiteMatch :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmtList fields runtime\n+ [Stmt.ite cond thenBranch elseBranch])\n+ (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n+ state compiledIR) := by\n+ have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_else\n+ (fields := fields) (runtime := runtime) (state := state)\n+ (scope := scope) (cond := cond)\n+ (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n+ (extraFuel := wholeExtraFuel) (tempName := tempName)\n+ (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n+ (tailIR := []) (condValue := condVal)\n+ (sourceCondValue := condVal)\n+ helse helseSem' hCondSrc\n+ (by simp [hcondZero])\n+ hcondEval hcondZero rfl\n+ simp only [List.append_nil] at this\n+ exact this\n+ -- execStmt (.ite ...) = execStmtList elseBranch (by source semantics)\n+ have hexecStmtElse : SourceSemantics.execStmt fields runtime\n+ (Stmt.ite cond thenBranch elseBranch) =\n+ SourceSemantics.execStmtList fields runtime elseBranch := by\n+ simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n+ -- execStmtList [.ite ...] = execStmtList elseBranch (by terminal_ite_else_eq)\n+ have hsourceEq :=\n+ FunctionBody.execStmtList_terminal_core_ite_else_eq\n+ (fields := fields) (runtime := runtime) (scope := scope)\n+ (cond := cond) (thenBranch := thenBranch)\n+ (elseBranch := elseBranch) (rest := [])\n+ (condValue := condVal) helse hCondSrc\n+ (by simp [hcondZero])\n+ -- Rewrite hiteMatch source from execStmtList [.ite ...] to execStmtList elseBranch\n+ rw [hsourceEq] at hiteMatch\n+ -- Now hiteMatch : stmtResultMatchesIRExec fields\n+ -- (execStmtList fields runtime elseBranch) (execIRStmts ... state compiledIR)\n+ -- Convert to stmtResultMatchesIRExec about execStmt\n+ have hbodyMatch :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmt fields runtime\n+ (Stmt.ite cond thenBranch elseBranch))\n+ (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n+ rw [hexecStmtElse, hwholeFuel]; exact hiteMatch\n+ refine ⟨_, _, rfl, rfl, ?_⟩\n+ exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n+ hbodyMatch\n+ (by rw [hexecStmtElse]\n+ exact FunctionBody.execStmtList_terminal_core_not_continue\n+ (fields := fields) (runtime := runtime) (scope := scope)\n+ (stmts := elseBranch) helse)\n+ · -- Condition is nonzero → take then branch\n+ have hBindIte :=\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n+ (scope := scope) (inScopeNames := scope)\n+ (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n+ (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n+ have hRuntimeIte :=\n+ FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n+ (name := tempName) (value := condVal) hruntime\n+ have hThen5 : sizeOf thenIR + 5 ≤ sizeOf compiledIR := by\n+ change sizeOf thenIR + 5 ≤ sizeOf compiledIR\n+ simp_wf\n+ omega\n+ let branchExtraFuel :=\n+ sizeOf compiledIR - (sizeOf thenIR + 5) + wholeExtraFuel\n+ rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n+ (fields := fields) (runtime := runtime)\n+ (state := state.setVar tempName condVal) (scope := scope)\n+ (inScopeNames := scope) (stmts := thenBranch)\n+ (extraFuel := branchExtraFuel)\n+ hthen\n+ FunctionBody.scopeNamesIncluded_refl\n+ hscope hBindIte hbounded hRuntimeIte with\n+ ⟨thenIR', hthenIR', hthenSem⟩\n+ rw [hthenIR] at hthenIR'\n+ have hthenEq : thenIR' = thenIR := (Except.ok.inj hthenIR').symm\n+ rw [show thenIR' = thenIR from hthenEq] at hthenSem\n+ -- Fuel alignment for then branch (has +1 on both sides, so direct)\n+ have hthenSem' :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmtList fields runtime thenBranch)\n+ (execIRStmts (sizeOf thenIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n+ (sizeOf thenIR + 5) + wholeExtraFuel) + 1)\n+ (state.setVar tempName condVal) thenIR) := by\n+ simp only [List.append_nil, branchExtraFuel] at hthenSem ⊢\n+ exact hthenSem\n+ -- Apply _ite_then to get match for the whole ITE statement list\n+ have hiteMatch :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmtList fields runtime\n+ [Stmt.ite cond thenBranch elseBranch])\n+ (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n+ state compiledIR) := by\n+ have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_then\n+ (fields := fields) (runtime := runtime) (state := state)\n+ (scope := scope) (cond := cond)\n+ (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n+ (extraFuel := wholeExtraFuel) (tempName := tempName)\n+ (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n+ (tailIR := []) (condValue := condVal)\n+ (sourceCondValue := condVal)\n+ hthen hthenSem' hCondSrc\n+ (by simp [hcondZero])\n+ hcondEval\n+ (by intro hzero; exact hcondZero hzero) rfl\n+ simp only [List.append_nil] at this\n+ exact this\n+ -- execStmt (.ite ...) = execStmtList thenBranch (by source semantics)\n+ have hexecStmtThen : SourceSemantics.execStmt fields runtime\n+ (Stmt.ite cond thenBranch elseBranch) =\n+ SourceSemantics.execStmtList fields runtime thenBranch := by\n+ simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n+ -- execStmtList [.ite ...] = execStmtList thenBranch\n+ have hsourceEq :=\n+ FunctionBody.execStmtList_terminal_core_ite_then_eq\n+ (fields := fields) (runtime := runtime) (scope := scope)\n+ (cond := cond) (thenBranch := thenBranch)\n+ (elseBranch := elseBranch) (rest := [])\n+ (condValue := condVal) hthen hCondSrc\n+ (by simp [hcondZero])\n+ rw [hsourceEq] at hiteMatch\n+ have hbodyMatch :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmt fields runtime\n+ (Stmt.ite cond thenBranch elseBranch))\n+ (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n+ rw [hexecStmtThen, hwholeFuel]; exact hiteMatch\n+ refine ⟨_, _, rfl, rfl, ?_⟩\n+ exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n+ hbodyMatch\n+ (by rw [hexecStmtThen]\n+ exact FunctionBody.execStmtList_terminal_core_not_continue\n+ (fields := fields) (runtime := runtime) (scope := scope)\n+ (stmts := thenBranch) hthen)\n \n set_option maxHeartbeats 800000 in\n private theorem compiledStmtStep_letStorageField\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21340,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_67"},"challenge_id":{"kind":"string","value":"91aebdb5b7e89c96"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":67,"string":"67"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface","depth":1,"n_commands":0,"n_lines":8,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction stmts with\n | nil => simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites]\n | cons stmt rest ih =>\n have hsplit := Bool.or_eq_false_iff.mp hsurface\n simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites,\n stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface hsplit.1,\n ih hsplit.2]","n_chars":382,"n_subproofs":1,"n_tactics":8,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 8,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction stmts with\\n | nil => simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites]\\n | cons stmt rest ih =>\\n have hsplit := Bool.or_eq_false_iff.mp hsurface\\n simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites,\\n stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface hsplit.1,\\n ih hsplit.2]\",\n \"n_chars\": 382,\n \"n_subproofs\": 1,\n \"n_tactics\": 8,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface","text":"private theorem stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\n {stmt : Stmt}\n (hsurface : stmtTouchesUnsupportedContractSurface stmt = false) :\n stmtTouchesUnsupportedContractSurfaceExceptMappingWrites stmt = false := by\n cases stmt <;> simp [stmtTouchesUnsupportedContractSurfaceExceptMappingWrites,\n stmtTouchesUnsupportedContractSurface] at hsurface ⊢\n all_goals assumption\n\n","fan_in":1,"n_lines":9,"n_chars":433,"n_subproofs":0,"n_tactics":5,"cyclomatic":3,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\",\n \"text\": \"private theorem stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\\n {stmt : Stmt}\\n (hsurface : stmtTouchesUnsupportedContractSurface stmt = false) :\\n stmtTouchesUnsupportedContractSurfaceExceptMappingWrites stmt = false := by\\n cases stmt <;> simp [stmtTouchesUnsupportedContractSurfaceExceptMappingWrites,\\n stmtTouchesUnsupportedContractSurface] at hsurface ⊢\\n all_goals assumption\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 9,\n \"n_chars\": 433,\n \"n_subproofs\": 0,\n \"n_tactics\": 5,\n \"cyclomatic\": 3,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":13,"n_chars":661,"n_subproofs":1,"n_tactics":8,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 13,\n \"n_chars\": 661,\n \"n_subproofs\": 1,\n \"n_tactics\": 8,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\ntheorem stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\n {stmts : List Stmt}\n (hsurface : stmtListTouchesUnsupportedContractSurface stmts = false) :\n stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites stmts = false := by\n induction stmts with\n | nil => simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites]\n | cons stmt rest ih => sorry\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\n {stmt : Stmt}\n (hsurface : stmtTouchesUnsupportedContractSurface stmt = false) :\n stmtTouchesUnsupportedContractSurfaceExceptMappingWrites stmt = false := by\n cases stmt <;> simp [stmtTouchesUnsupportedContractSurfaceExceptMappingWrites,\n stmtTouchesUnsupportedContractSurface] at hsurface ⊢\n all_goals assumption\n\ntheorem stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\n {stmts : List Stmt}\n (hsurface : stmtListTouchesUnsupportedContractSurface stmts = false) :\n stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites stmts = false := by\n induction stmts with\n | nil => simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites]\n | cons stmt rest ih =>\n have hsplit := Bool.or_eq_false_iff.mp hsurface\n simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites,\n stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface hsplit.1,\n ih hsplit.2]\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -1925,13 +1925,25 @@\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n \n+private theorem stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\n+ {stmt : Stmt}\n+ (hsurface : stmtTouchesUnsupportedContractSurface stmt = false) :\n+ stmtTouchesUnsupportedContractSurfaceExceptMappingWrites stmt = false := by\n+ cases stmt <;> simp [stmtTouchesUnsupportedContractSurfaceExceptMappingWrites,\n+ stmtTouchesUnsupportedContractSurface] at hsurface ⊢\n+ all_goals assumption\n+\n theorem stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\n {stmts : List Stmt}\n (hsurface : stmtListTouchesUnsupportedContractSurface stmts = false) :\n stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites stmts = false := by\n induction stmts with\n | nil => simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites]\n- | cons stmt rest ih => sorry\n+ | cons stmt rest ih =>\n+ have hsplit := Bool.or_eq_false_iff.mp hsurface\n+ simp [stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites,\n+ stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface hsplit.1,\n+ ih hsplit.2]\n \n set_option maxHeartbeats 800000 in\n private theorem compiledStmtStep_letStorageField\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21341,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_68"},"challenge_id":{"kind":"string","value":"f24a4f10592d8415"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":68,"string":"68"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member","depth":1,"n_commands":0,"n_lines":45,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite","n_chars":2292,"n_subproofs":5,"n_tactics":41,"cyclomatic":5,"n_automation":11,"n_rewrites":3,"n_structural":12,"automation_only":false,"max_nesting":16},{"theorem_name":"findResolvedFieldAtSlotCopyFrom_of_member","depth":1,"n_commands":0,"n_lines":66,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite","n_chars":3248,"n_subproofs":5,"n_tactics":66,"cyclomatic":6,"n_automation":17,"n_rewrites":11,"n_structural":15,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"theorem_name\": \"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 45,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction fields generalizing seen idx with\\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\\n | cons field rest ih =>\\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\\n simp only [firstFieldWriteSlotConflictCopyFrom]\\n by_cases hname : field.name == fieldName\\n · -- field.name matches: hfind and hwrite resolve here\\n simp [hname] at hfind hwrite\\n obtain ⟨rfl, rfl⟩ := hfind\\n subst hwrite\\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\\n -- and all packed bits = field.packedBits = none\\n have htarget_in_entries :\\n SourceSemantics.wordNormalize targetSlot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n simp only [List.mem_cons] at hslot\\n rcases hslot with hslot | halias\\n · subst targetSlot\\n exact fieldWriteEntriesAt_base_mem idx field\\n · exact fieldWriteEntriesAt_alias_mem halias\\n have hunpacked_entries :\\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\\n packed = none := by\\n intro packed hmem\\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\\n hseen htarget_in_entries hunpacked_entries\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | none => exact absurd hc hconflict\\n | some _ => simp\\n · -- field.name doesn't match: recurse\\n simp [hname] at hfind hwrite\\n have hseen' :\\n SourceSemantics.wordNormalize targetSlot ∈\\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\\n (fun entry => entry.1) := by\\n rw [List.map_append, List.mem_append]\\n exact Or.inr hseen\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | some _ => simp\\n | none => exact ih hseen' hfind hwrite\",\n \"n_chars\": 2292,\n \"n_subproofs\": 5,\n \"n_tactics\": 41,\n \"cyclomatic\": 5,\n \"n_automation\": 11,\n \"n_rewrites\": 3,\n \"n_structural\": 12,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"findResolvedFieldAtSlotCopyFrom_of_member\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 66,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction fields generalizing seen idx with\\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\\n | cons field rest ih =>\\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\\n simp only [findResolvedFieldAtSlotCopyFrom]\\n by_cases hname : field.name == fieldName\\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\\n simp [hname] at hfind hwrite\\n obtain ⟨rfl, rfl⟩ := hfind\\n subst writeSlots\\n simp only [List.mem_cons] at hslot\\n rcases hslot with rfl | hmem\\n · simp\\n · rw [show\\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\\n (SourceSemantics.wordNormalize targetSlot) = true by\\n rw [List.contains_eq_mem]\\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\\n simp\\n · -- field.name doesn't match: recurse\\n simp [hname] at hfind hwrite\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\\n | none =>\\n rw [hc] at hnoConflict\\n -- After simp, condition is Prop-level: = or ∈\\n by_cases hcapture :\\n SourceSemantics.wordNormalize (field.slot.getD idx) =\\n SourceSemantics.wordNormalize targetSlot ∨\\n ∃ a ∈ field.aliasSlots,\\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\\n · exfalso\\n have htargetInEntries :\\n SourceSemantics.wordNormalize targetSlot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\\n · have hb := fieldWriteEntriesAt_base_mem idx field\\n rw [hbase] at hb\\n exact hb\\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\\n rw [haEq] at haIn\\n exact haIn\\n have htargetInSeen :\\n SourceSemantics.wordNormalize targetSlot ∈\\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\\n (fun entry => entry.1) := by\\n rw [List.map_append, List.mem_append, List.map_reverse]\\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\\n · push_neg at hcapture\\n rw [show\\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\\n SourceSemantics.wordNormalize targetSlot) ||\\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\\n (SourceSemantics.wordNormalize targetSlot)) = false by\\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\\n List.contains_eq_mem, List.mem_map]\\n exact ⟨hcapture.1, by\\n intro hmem\\n rcases hmem with ⟨a, haMem, haEq⟩\\n exact hcapture.2 a haMem haEq⟩]\\n exact ih hnoConflict hfind hwrite\",\n \"n_chars\": 3248,\n \"n_subproofs\": 5,\n \"n_tactics\": 66,\n \"cyclomatic\": 6,\n \"n_automation\": 17,\n \"n_rewrites\": 11,\n \"n_structural\": 15,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"fieldWriteEntriesAt_alias_mem","text":"private theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\n","fan_in":2,"n_lines":39,"n_chars":1971,"n_subproofs":2,"n_tactics":33,"cyclomatic":2,"n_automation":27,"n_rewrites":0,"n_structural":10,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"fieldWriteEntriesAt_alias_mem\",\n \"text\": \"private theorem fieldWriteEntriesAt_alias_mem\\n {idx : Nat} {field : Field} {slot : Nat}\\n (hmem : slot ∈ field.aliasSlots) :\\n SourceSemantics.wordNormalize slot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\\n exists_mem_zipIdx_of_mem hmem\\n cases ty with\\n | uint256 =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | address =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | adt _ maxFields =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨s!\\\"{name}.aliasSlots[{aliasIdx}]\\\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\\n | dynamicArray _ =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | mappingTyped _ =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | mappingStruct _ _ =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | mappingStruct2 _ _ _ =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 39,\n \"n_chars\": 1971,\n \"n_subproofs\": 2,\n \"n_tactics\": 33,\n \"cyclomatic\": 2,\n \"n_automation\": 27,\n \"n_rewrites\": 0,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStep_assignStorageField","fan_in":1,"n_deps_direct":5,"n_deps_transitive":24,"n_lines":69,"n_chars":4251,"n_subproofs":7,"n_tactics":64,"cyclomatic":5,"n_automation":18,"n_rewrites":8,"n_structural":9,"automation_only":false,"max_nesting":14}],"string":"[\n {\n \"name\": \"compiledStmtStep_assignStorageField\",\n \"fan_in\": 1,\n \"n_deps_direct\": 5,\n \"n_deps_transitive\": 24,\n \"n_lines\": 69,\n \"n_chars\": 4251,\n \"n_subproofs\": 7,\n \"n_tactics\": 64,\n \"cyclomatic\": 5,\n \"n_automation\": 18,\n \"n_rewrites\": 8,\n \"n_structural\": 9,\n \"automation_only\": false,\n \"max_nesting\": 14\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":18,"string":"18"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · sorry\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · sorry\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nprivate theorem compiledStmtStep_assignStorageField\n {fields : List Field}\n {scope : List String}\n {name fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storage fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storage fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nprivate theorem compiledStmtStep_assignStorageField\n {fields : List Field}\n {scope : List String}\n {name fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storage fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storage fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -309,6 +309,44 @@\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n \n+private theorem fieldWriteEntriesAt_alias_mem\n+ {idx : Nat} {field : Field} {slot : Nat}\n+ (hmem : slot ∈ field.aliasSlots) :\n+ SourceSemantics.wordNormalize slot ∈\n+ (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n+ obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n+ obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n+ exists_mem_zipIdx_of_mem hmem\n+ cases ty with\n+ | uint256 =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | address =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | adt _ maxFields =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n+ | dynamicArray _ =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | mappingTyped _ =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | mappingStruct _ _ =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | mappingStruct2 _ _ _ =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+\n private theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n@@ -450,7 +488,7 @@\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n- · sorry\n+ · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n@@ -529,7 +567,9 @@\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n- · sorry\n+ · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n+ rw [haEq] at haIn\n+ exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21342,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_69"},"challenge_id":{"kind":"string","value":"843895de6034f8f0"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":69,"string":"69"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member","depth":1,"n_commands":0,"n_lines":45,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite","n_chars":2292,"n_subproofs":5,"n_tactics":41,"cyclomatic":5,"n_automation":11,"n_rewrites":3,"n_structural":12,"automation_only":false,"max_nesting":16},{"theorem_name":"findResolvedFieldAtSlotCopyFrom_of_member","depth":1,"n_commands":0,"n_lines":66,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite","n_chars":3248,"n_subproofs":5,"n_tactics":66,"cyclomatic":6,"n_automation":17,"n_rewrites":11,"n_structural":15,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"theorem_name\": \"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 45,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction fields generalizing seen idx with\\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\\n | cons field rest ih =>\\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\\n simp only [firstFieldWriteSlotConflictCopyFrom]\\n by_cases hname : field.name == fieldName\\n · -- field.name matches: hfind and hwrite resolve here\\n simp [hname] at hfind hwrite\\n obtain ⟨rfl, rfl⟩ := hfind\\n subst hwrite\\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\\n -- and all packed bits = field.packedBits = none\\n have htarget_in_entries :\\n SourceSemantics.wordNormalize targetSlot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n simp only [List.mem_cons] at hslot\\n rcases hslot with hslot | halias\\n · subst targetSlot\\n exact fieldWriteEntriesAt_base_mem idx field\\n · exact fieldWriteEntriesAt_alias_mem halias\\n have hunpacked_entries :\\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\\n packed = none := by\\n intro packed hmem\\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\\n hseen htarget_in_entries hunpacked_entries\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | none => exact absurd hc hconflict\\n | some _ => simp\\n · -- field.name doesn't match: recurse\\n simp [hname] at hfind hwrite\\n have hseen' :\\n SourceSemantics.wordNormalize targetSlot ∈\\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\\n (fun entry => entry.1) := by\\n rw [List.map_append, List.mem_append]\\n exact Or.inr hseen\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | some _ => simp\\n | none => exact ih hseen' hfind hwrite\",\n \"n_chars\": 2292,\n \"n_subproofs\": 5,\n \"n_tactics\": 41,\n \"cyclomatic\": 5,\n \"n_automation\": 11,\n \"n_rewrites\": 3,\n \"n_structural\": 12,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"findResolvedFieldAtSlotCopyFrom_of_member\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 66,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction fields generalizing seen idx with\\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\\n | cons field rest ih =>\\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\\n simp only [findResolvedFieldAtSlotCopyFrom]\\n by_cases hname : field.name == fieldName\\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\\n simp [hname] at hfind hwrite\\n obtain ⟨rfl, rfl⟩ := hfind\\n subst writeSlots\\n simp only [List.mem_cons] at hslot\\n rcases hslot with rfl | hmem\\n · simp\\n · rw [show\\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\\n (SourceSemantics.wordNormalize targetSlot) = true by\\n rw [List.contains_eq_mem]\\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\\n simp\\n · -- field.name doesn't match: recurse\\n simp [hname] at hfind hwrite\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\\n | none =>\\n rw [hc] at hnoConflict\\n -- After simp, condition is Prop-level: = or ∈\\n by_cases hcapture :\\n SourceSemantics.wordNormalize (field.slot.getD idx) =\\n SourceSemantics.wordNormalize targetSlot ∨\\n ∃ a ∈ field.aliasSlots,\\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\\n · exfalso\\n have htargetInEntries :\\n SourceSemantics.wordNormalize targetSlot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\\n · have hb := fieldWriteEntriesAt_base_mem idx field\\n rw [hbase] at hb\\n exact hb\\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\\n rw [haEq] at haIn\\n exact haIn\\n have htargetInSeen :\\n SourceSemantics.wordNormalize targetSlot ∈\\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\\n (fun entry => entry.1) := by\\n rw [List.map_append, List.mem_append, List.map_reverse]\\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\\n · push_neg at hcapture\\n rw [show\\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\\n SourceSemantics.wordNormalize targetSlot) ||\\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\\n (SourceSemantics.wordNormalize targetSlot)) = false by\\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\\n List.contains_eq_mem, List.mem_map]\\n exact ⟨hcapture.1, by\\n intro hmem\\n rcases hmem with ⟨a, haMem, haEq⟩\\n exact hcapture.2 a haMem haEq⟩]\\n exact ih hnoConflict hfind hwrite\",\n \"n_chars\": 3248,\n \"n_subproofs\": 5,\n \"n_tactics\": 66,\n \"cyclomatic\": 6,\n \"n_automation\": 17,\n \"n_rewrites\": 11,\n \"n_structural\": 15,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"fieldWriteEntriesAt_alias_mem","text":"private theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\n","fan_in":2,"n_lines":39,"n_chars":1971,"n_subproofs":2,"n_tactics":33,"cyclomatic":2,"n_automation":27,"n_rewrites":0,"n_structural":10,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"fieldWriteEntriesAt_alias_mem\",\n \"text\": \"private theorem fieldWriteEntriesAt_alias_mem\\n {idx : Nat} {field : Field} {slot : Nat}\\n (hmem : slot ∈ field.aliasSlots) :\\n SourceSemantics.wordNormalize slot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\\n exists_mem_zipIdx_of_mem hmem\\n cases ty with\\n | uint256 =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | address =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | adt _ maxFields =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨s!\\\"{name}.aliasSlots[{aliasIdx}]\\\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\\n | dynamicArray _ =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | mappingTyped _ =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | mappingStruct _ _ =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n | mappingStruct2 _ _ _ =>\\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\\n SourceSemantics.wordNormalize]\\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 39,\n \"n_chars\": 1971,\n \"n_subproofs\": 2,\n \"n_tactics\": 33,\n \"cyclomatic\": 2,\n \"n_automation\": 27,\n \"n_rewrites\": 0,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListGenericCore_singleton_assignStorageField","fan_in":0,"n_deps_direct":1,"n_deps_transitive":25,"n_lines":15,"n_chars":604,"n_subproofs":0,"n_tactics":3,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"stmtListGenericCore_singleton_assignStorageField\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 25,\n \"n_lines\": 15,\n \"n_chars\": 604,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":19,"string":"19"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · sorry\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · sorry\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nprivate theorem compiledStmtStep_assignStorageField\n {fields : List Field}\n {scope : List String}\n {name fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storage fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storage fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\ntheorem stmtListGenericCore_singleton_assignStorageField\n {fields : List Field}\n {scope : List String}\n {name fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n StmtListGenericCore fields scope [Stmt.assignVar name (Expr.storage fieldName)] :=\n StmtListGenericCore.cons\n (compiledStmtStep_assignStorageField hnoConflict hfind hfieldInScope)\n StmtListGenericCore.nil\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nprivate theorem compiledStmtStep_assignStorageField\n {fields : List Field}\n {scope : List String}\n {name fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storage fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storage fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\ntheorem stmtListGenericCore_singleton_assignStorageField\n {fields : List Field}\n {scope : List String}\n {name fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n StmtListGenericCore fields scope [Stmt.assignVar name (Expr.storage fieldName)] :=\n StmtListGenericCore.cons\n (compiledStmtStep_assignStorageField hnoConflict hfind hfieldInScope)\n StmtListGenericCore.nil\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -309,6 +309,44 @@\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n \n+private theorem fieldWriteEntriesAt_alias_mem\n+ {idx : Nat} {field : Field} {slot : Nat}\n+ (hmem : slot ∈ field.aliasSlots) :\n+ SourceSemantics.wordNormalize slot ∈\n+ (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n+ obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n+ obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n+ exists_mem_zipIdx_of_mem hmem\n+ cases ty with\n+ | uint256 =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | address =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | adt _ maxFields =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n+ | dynamicArray _ =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | mappingTyped _ =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | mappingStruct _ _ =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+ | mappingStruct2 _ _ _ =>\n+ simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n+ SourceSemantics.wordNormalize]\n+ exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n+\n private theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n@@ -450,7 +488,7 @@\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n- · sorry\n+ · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n@@ -529,7 +567,9 @@\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n- · sorry\n+ · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n+ rw [haEq] at haIn\n+ exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21343,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_70"},"challenge_id":{"kind":"string","value":"eedf2ed12d1c359c"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":70,"string":"70"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":14,"string":"14"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compiledStmtStep_mstore_single","depth":1,"n_commands":0,"n_lines":7,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n hoffsetIRInternal, hvalueIRInternal, Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_mstore_single_preserves\n hcoreOffset hinScopeOffset hcoreValue hinScopeValue hoffsetIR hvalueIR","n_chars":440,"n_subproofs":2,"n_tactics":7,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_tstore_single","depth":1,"n_commands":0,"n_lines":7,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n hoffsetIRInternal, hvalueIRInternal, Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_tstore_single_preserves\n hcoreOffset hinScopeOffset hcoreValue hinScopeValue hoffsetIR hvalueIR","n_chars":440,"n_subproofs":2,"n_tactics":7,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMappingUint_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR","n_chars":729,"n_subproofs":2,"n_tactics":11,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compileExprList_core_ok","depth":1,"n_commands":0,"n_lines":19,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction exprs with\n | nil =>\n exact ⟨[], by\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\n pure, Except.pure]⟩\n | cons expr rest ih =>\n have hhead : FunctionBody.ExprCompileCore expr := hcore expr (by simp)\n have htail : ∀ e ∈ rest, FunctionBody.ExprCompileCore e := by\n intro e he\n exact hcore e (by simp [he])\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hhead with ⟨exprIR, hexprIR⟩\n rcases ih htail with ⟨restIR, hrestIR⟩\n have hexprIRInternal := compileExprWithInternals_nil_ok hexprIR\n have hrestIRInternal := compileExprListWithInternals_nil_ok hrestIR\n exact ⟨exprIR :: restIR, by\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\n hexprIRInternal, hrestIRInternal, bind, Except.bind, pure, Except.pure]\n ⟩","n_chars":930,"n_subproofs":4,"n_tactics":19,"cyclomatic":4,"n_automation":4,"n_rewrites":0,"n_structural":7,"automation_only":false,"max_nesting":10},{"theorem_name":"eval_compileExprList_core_of_scope","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction exprs generalizing exprIRs with\n | nil =>\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals] at hcompiled\n cases hcompiled\n exact ⟨[], rfl, .nil⟩\n | cons expr rest ih =>\n have hhead : FunctionBody.ExprCompileCore expr := hcore expr (by simp)\n have htail :\n ∀ expr' ∈ rest, FunctionBody.ExprCompileCore expr' := by\n intro expr' hexpr'\n exact hcore expr' (by simp [hexpr'])\n have htailScope :\n ∀ expr' ∈ rest, FunctionBody.exprBoundNamesInScope expr' scope := by\n intro expr' hexpr'\n exact hinScope expr' (by simp [hexpr'])\n rcases compileExprList_core_ok (fields := fields) htail with ⟨restIRs, hrestIRs⟩\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hhead with ⟨exprIR, hexprIR⟩\n have hexprIRInternal := compileExprWithInternals_nil_ok hexprIR\n have hrestIRsInternal := compileExprListWithInternals_nil_ok hrestIRs\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\n hexprIRInternal, hrestIRsInternal] at hcompiled\n injection hcompiled with hcompiledTail\n subst hcompiledTail\n rcases eval_compileExpr_core_some_of_scope\n (expr := expr) (exprIR := exprIR) hhead hexact (hinScope expr (by simp))\n hbounded hscope hruntime hexprIR with\n ⟨headVal, hheadVal, hheadEval⟩\n rcases ih htail htailScope hrestIRs with\n ⟨restVals, hrestVals, hrestEval⟩\n refine ⟨headVal :: restVals, ?_, ?_⟩\n · simp [SourceSemantics.evalExprList, hheadVal, hrestVals]\n · exact .cons hheadEval hrestEval","n_chars":1688,"n_subproofs":5,"n_tactics":33,"cyclomatic":7,"n_automation":8,"n_rewrites":1,"n_structural":13,"automation_only":false,"max_nesting":10},{"theorem_name":"compiledStmtStep_setMappingChain_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRsInternal := compileExprListWithInternals_nil_ok hkeyIRs\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMappingChain,\n hmapping, hwriteSlots, hkeyIRsInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMappingChain_singleSlot_of_slotSafety_preserves\n hcoreKeys hinScopeKeys hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIRs hvalueIR","n_chars":739,"n_subproofs":2,"n_tactics":11,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMapping_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMapping_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR","n_chars":725,"n_subproofs":2,"n_tactics":11,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMappingWord_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMappingWord_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR","n_chars":729,"n_subproofs":2,"n_tactics":11,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":14,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingPackedSlotWrite,\n hmapping, hpacked, hwriteSlots, hkeyIRInternal, hvalueIRInternal, Bool.not_true, bne_self_eq_false,\n ite_false, ite_true, pure, Except.pure, bind, Except.bind]\n simp [hfind, fieldLoadBuiltin, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue\n hcompatValue hcompatPacked hcompatSlotWord hcompatSlotCleared\n hpacked hwriteSlots hslotSafety hkeyIR hvalueIR","n_chars":945,"n_subproofs":2,"n_tactics":14,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setStructMember_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":13,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember,\n CompilationModel.compileMappingSlotWrite, hmapping, hnotMapping2, hmembers, hmember,\n hwriteSlots, hkeyIRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setStructMember_singleSlot_of_slotSafety_preserves\n hcoreKey hinScopeKey hcoreValue hinScopeValue hmembers hmember hwriteSlots\n hslotSafety hkeyIR hvalueIR","n_chars":831,"n_subproofs":2,"n_tactics":13,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMapping2_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":13,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMapping2,\n hmapping2, hwriteSlots, hkey1IRInternal, hkey2IRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMapping2_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR","n_chars":848,"n_subproofs":3,"n_tactics":13,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":13,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMapping2Word,\n hmapping2, hwriteSlots, hkey1IRInternal, hkey2IRInternal, hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR","n_chars":856,"n_subproofs":3,"n_tactics":13,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_setStructMember2_singleSlot_of_slotSafety","depth":1,"n_commands":0,"n_lines":14,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\n ⟨f, hfind, _⟩\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember2,\n hmapping2, hmembers, hmember, hwriteSlots, hkey1IRInternal, hkey2IRInternal,\n hvalueIRInternal]\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\n Bind.bind, Except.bind, pure, Except.pure]\n preserves := compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\n hmembers hmember hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR","n_chars":900,"n_subproofs":3,"n_tactics":14,"cyclomatic":2,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"compiledStmtStep_ite","depth":1,"n_commands":0,"n_lines":237,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcond with ⟨condIR, hcondIR⟩\n rcases FunctionBody.compileStmtList_terminal_core_ok\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := thenBranch)\n hthen with ⟨thenIR, hthenIR⟩\n rcases FunctionBody.compileStmtList_terminal_core_ok\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := elseBranch)\n helse with ⟨elseIR, helseIR⟩\n have helseNonempty : elseBranch.isEmpty = false := by\n cases elseBranch with\n | nil => exfalso; exact FunctionBody.stmtListTerminalCore_ne_nil helse rfl\n | cons => simp\n let tempName :=\n CompilationModel.pickFreshName \"__ite_cond\"\n (scope ++ collectExprNames cond ++\n collectStmtListNames thenBranch ++ collectStmtListNames elseBranch)\n let compiledIR :=\n [YulStmt.block\n [ YulStmt.let_ tempName condIR\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\n , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]]\n refine ⟨compiledIR, ?_⟩\n refine\n { compileOk := ?_\n preserves := ?_ }\n · show CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (.ite cond thenBranch elseBranch) = Except.ok compiledIR\n have hcondIRInternal := compileExprWithInternals_nil_ok hcondIR\n unfold CompilationModel.compileStmt CompilationModel.compileStmtWithFork\n simp [FunctionBody.compileStmtListWithFork_cancun_eq_compileStmtList,\n hcondIRInternal, hthenIR, helseIR, Except.bind, helseNonempty]\n simp [compiledIR, tempName, List.append_assoc, Bind.bind, Except.bind,\n Pure.pure, Except.pure]\n · intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n set wholeExtraFuel := extraFuel - (sizeOf compiledIR - compiledIR.length) with hWF\n have hsizeOf_eq : sizeOf compiledIR = 1 + sizeOf (YulStmt.block\n [ YulStmt.let_ tempName condIR\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\n , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]) + 1 := by\n rfl\n have hlength_eq : compiledIR.length = 1 := by rfl\n have hwholeFuel :\n compiledIR.length + extraFuel + 1 =\n sizeOf compiledIR + wholeExtraFuel + 1 := by\n rw [hWF, hsizeOf_eq, hlength_eq]\n have : sizeOf compiledIR - compiledIR.length ≤ extraFuel := hslack\n rw [hsizeOf_eq, hlength_eq] at this\n omega\n have hpresent : FunctionBody.exprBoundNamesPresent cond runtime.bindings :=\n FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope\n -- Extract the Nat condition value via the eval bridge\n have heval := FunctionBody.eval_compileExpr_core_of_scope\n hcond hexact hinScope hbounded hpresent hruntime\n rw [hcondIR] at heval; simp [Except.toOption] at heval\n rcases hCondIRVal : evalIRExpr state condIR with _ | condVal\n · simp [hCondIRVal, Option.bind] at heval\n · simp [hCondIRVal, Option.bind] at heval\n have hCondSrc : SourceSemantics.evalExpr fields runtime cond = some condVal :=\n heval.symm\n have hcondEval : evalIRExpr state condIR = some condVal := hCondIRVal\n by_cases hcondZero : condVal = 0\n · -- Condition is zero → take else branch\n have hBindIte :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n (scope := scope) (inScopeNames := scope)\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n have hRuntimeIte :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := tempName) (value := condVal) hruntime\n have hElse6 : sizeOf elseIR + 6 ≤ sizeOf compiledIR := by\n change sizeOf elseIR + 6 ≤ sizeOf compiledIR\n simp_wf\n omega\n let branchExtraFuel :=\n sizeOf compiledIR - (sizeOf elseIR + 5) + wholeExtraFuel - 1\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n (fields := fields) (runtime := runtime)\n (state := state.setVar tempName condVal) (scope := scope)\n (inScopeNames := scope) (stmts := elseBranch)\n (extraFuel := branchExtraFuel)\n helse\n FunctionBody.scopeNamesIncluded_refl\n hscope hBindIte hbounded hRuntimeIte with\n ⟨elseIR', helseIR', helseSem⟩\n rw [helseIR] at helseIR'\n have helseEq : elseIR' = elseIR := (Except.ok.inj helseIR').symm\n rw [show elseIR' = elseIR from helseEq] at helseSem\n -- Fuel alignment: convert helseSem fuel to the form _ite_else expects\n have hfuelAlign : sizeOf elseIR + branchExtraFuel + 1 =\n sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf elseIR + 5) + wholeExtraFuel) := by\n simp only [List.append_nil, branchExtraFuel]\n have := hElse6\n omega\n have helseSem' :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime elseBranch)\n (execIRStmts (sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf elseIR + 5) + wholeExtraFuel))\n (state.setVar tempName condVal) elseIR) := by\n rw [← hfuelAlign]; exact helseSem\n -- Apply _ite_else to get match for the whole ITE statement list\n have hiteMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime\n [Stmt.ite cond thenBranch elseBranch])\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n state compiledIR) := by\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_else\n (fields := fields) (runtime := runtime) (state := state)\n (scope := scope) (cond := cond)\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n (extraFuel := wholeExtraFuel) (tempName := tempName)\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n (tailIR := []) (condValue := condVal)\n (sourceCondValue := condVal)\n helse helseSem' hCondSrc\n (by simp [hcondZero])\n hcondEval hcondZero rfl\n simp only [List.append_nil] at this\n exact this\n -- execStmt (.ite ...) = execStmtList elseBranch (by source semantics)\n have hexecStmtElse : SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch) =\n SourceSemantics.execStmtList fields runtime elseBranch := by\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n -- execStmtList [.ite ...] = execStmtList elseBranch (by terminal_ite_else_eq)\n have hsourceEq :=\n FunctionBody.execStmtList_terminal_core_ite_else_eq\n (fields := fields) (runtime := runtime) (scope := scope)\n (cond := cond) (thenBranch := thenBranch)\n (elseBranch := elseBranch) (rest := [])\n (condValue := condVal) helse hCondSrc\n (by simp [hcondZero])\n -- Rewrite hiteMatch source from execStmtList [.ite ...] to execStmtList elseBranch\n rw [hsourceEq] at hiteMatch\n -- Now hiteMatch : stmtResultMatchesIRExec fields\n -- (execStmtList fields runtime elseBranch) (execIRStmts ... state compiledIR)\n -- Convert to stmtResultMatchesIRExec about execStmt\n have hbodyMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch))\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n rw [hexecStmtElse, hwholeFuel]; exact hiteMatch\n refine ⟨_, _, rfl, rfl, ?_⟩\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n hbodyMatch\n (by rw [hexecStmtElse]\n exact FunctionBody.execStmtList_terminal_core_not_continue\n (fields := fields) (runtime := runtime) (scope := scope)\n (stmts := elseBranch) helse)\n · -- Condition is nonzero → take then branch\n have hBindIte :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n (scope := scope) (inScopeNames := scope)\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n have hRuntimeIte :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := tempName) (value := condVal) hruntime\n have hThen5 : sizeOf thenIR + 5 ≤ sizeOf compiledIR := by\n change sizeOf thenIR + 5 ≤ sizeOf compiledIR\n simp_wf\n omega\n let branchExtraFuel :=\n sizeOf compiledIR - (sizeOf thenIR + 5) + wholeExtraFuel\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n (fields := fields) (runtime := runtime)\n (state := state.setVar tempName condVal) (scope := scope)\n (inScopeNames := scope) (stmts := thenBranch)\n (extraFuel := branchExtraFuel)\n hthen\n FunctionBody.scopeNamesIncluded_refl\n hscope hBindIte hbounded hRuntimeIte with\n ⟨thenIR', hthenIR', hthenSem⟩\n rw [hthenIR] at hthenIR'\n have hthenEq : thenIR' = thenIR := (Except.ok.inj hthenIR').symm\n rw [show thenIR' = thenIR from hthenEq] at hthenSem\n -- Fuel alignment for then branch (has +1 on both sides, so direct)\n have hthenSem' :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime thenBranch)\n (execIRStmts (sizeOf thenIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf thenIR + 5) + wholeExtraFuel) + 1)\n (state.setVar tempName condVal) thenIR) := by\n simp only [List.append_nil, branchExtraFuel] at hthenSem ⊢\n exact hthenSem\n -- Apply _ite_then to get match for the whole ITE statement list\n have hiteMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime\n [Stmt.ite cond thenBranch elseBranch])\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n state compiledIR) := by\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_then\n (fields := fields) (runtime := runtime) (state := state)\n (scope := scope) (cond := cond)\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n (extraFuel := wholeExtraFuel) (tempName := tempName)\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n (tailIR := []) (condValue := condVal)\n (sourceCondValue := condVal)\n hthen hthenSem' hCondSrc\n (by simp [hcondZero])\n hcondEval\n (by intro hzero; exact hcondZero hzero) rfl\n simp only [List.append_nil] at this\n exact this\n -- execStmt (.ite ...) = execStmtList thenBranch (by source semantics)\n have hexecStmtThen : SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch) =\n SourceSemantics.execStmtList fields runtime thenBranch := by\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n -- execStmtList [.ite ...] = execStmtList thenBranch\n have hsourceEq :=\n FunctionBody.execStmtList_terminal_core_ite_then_eq\n (fields := fields) (runtime := runtime) (scope := scope)\n (cond := cond) (thenBranch := thenBranch)\n (elseBranch := elseBranch) (rest := [])\n (condValue := condVal) hthen hCondSrc\n (by simp [hcondZero])\n rw [hsourceEq] at hiteMatch\n have hbodyMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch))\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n rw [hexecStmtThen, hwholeFuel]; exact hiteMatch\n refine ⟨_, _, rfl, rfl, ?_⟩\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n hbodyMatch\n (by rw [hexecStmtThen]\n exact FunctionBody.execStmtList_terminal_core_not_continue\n (fields := fields) (runtime := runtime) (scope := scope)\n (stmts := thenBranch) hthen)","n_chars":12831,"n_subproofs":32,"n_tactics":230,"cyclomatic":8,"n_automation":29,"n_rewrites":20,"n_structural":25,"automation_only":false,"max_nesting":18}],"string":"[\n {\n \"theorem_name\": \"compiledStmtStep_mstore_single\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 7,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\\n hoffsetIRInternal, hvalueIRInternal, Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_mstore_single_preserves\\n hcoreOffset hinScopeOffset hcoreValue hinScopeValue hoffsetIR hvalueIR\",\n \"n_chars\": 440,\n \"n_subproofs\": 2,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_tstore_single\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 7,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\\n hoffsetIRInternal, hvalueIRInternal, Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_tstore_single_preserves\\n hcoreOffset hinScopeOffset hcoreValue hinScopeValue hoffsetIR hvalueIR\",\n \"n_chars\": 440,\n \"n_subproofs\": 2,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingUint_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 729,\n \"n_subproofs\": 2,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compileExprList_core_ok\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 19,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction exprs with\\n | nil =>\\n exact ⟨[], by\\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\\n pure, Except.pure]⟩\\n | cons expr rest ih =>\\n have hhead : FunctionBody.ExprCompileCore expr := hcore expr (by simp)\\n have htail : ∀ e ∈ rest, FunctionBody.ExprCompileCore e := by\\n intro e he\\n exact hcore e (by simp [he])\\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hhead with ⟨exprIR, hexprIR⟩\\n rcases ih htail with ⟨restIR, hrestIR⟩\\n have hexprIRInternal := compileExprWithInternals_nil_ok hexprIR\\n have hrestIRInternal := compileExprListWithInternals_nil_ok hrestIR\\n exact ⟨exprIR :: restIR, by\\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\\n hexprIRInternal, hrestIRInternal, bind, Except.bind, pure, Except.pure]\\n ⟩\",\n \"n_chars\": 930,\n \"n_subproofs\": 4,\n \"n_tactics\": 19,\n \"cyclomatic\": 4,\n \"n_automation\": 4,\n \"n_rewrites\": 0,\n \"n_structural\": 7,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"eval_compileExprList_core_of_scope\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction exprs generalizing exprIRs with\\n | nil =>\\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals] at hcompiled\\n cases hcompiled\\n exact ⟨[], rfl, .nil⟩\\n | cons expr rest ih =>\\n have hhead : FunctionBody.ExprCompileCore expr := hcore expr (by simp)\\n have htail :\\n ∀ expr' ∈ rest, FunctionBody.ExprCompileCore expr' := by\\n intro expr' hexpr'\\n exact hcore expr' (by simp [hexpr'])\\n have htailScope :\\n ∀ expr' ∈ rest, FunctionBody.exprBoundNamesInScope expr' scope := by\\n intro expr' hexpr'\\n exact hinScope expr' (by simp [hexpr'])\\n rcases compileExprList_core_ok (fields := fields) htail with ⟨restIRs, hrestIRs⟩\\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hhead with ⟨exprIR, hexprIR⟩\\n have hexprIRInternal := compileExprWithInternals_nil_ok hexprIR\\n have hrestIRsInternal := compileExprListWithInternals_nil_ok hrestIRs\\n simp [CompilationModel.compileExprList, CompilationModel.compileExprListWithInternals,\\n hexprIRInternal, hrestIRsInternal] at hcompiled\\n injection hcompiled with hcompiledTail\\n subst hcompiledTail\\n rcases eval_compileExpr_core_some_of_scope\\n (expr := expr) (exprIR := exprIR) hhead hexact (hinScope expr (by simp))\\n hbounded hscope hruntime hexprIR with\\n ⟨headVal, hheadVal, hheadEval⟩\\n rcases ih htail htailScope hrestIRs with\\n ⟨restVals, hrestVals, hrestEval⟩\\n refine ⟨headVal :: restVals, ?_, ?_⟩\\n · simp [SourceSemantics.evalExprList, hheadVal, hrestVals]\\n · exact .cons hheadEval hrestEval\",\n \"n_chars\": 1688,\n \"n_subproofs\": 5,\n \"n_tactics\": 33,\n \"cyclomatic\": 7,\n \"n_automation\": 8,\n \"n_rewrites\": 1,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingChain_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRsInternal := compileExprListWithInternals_nil_ok hkeyIRs\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMappingChain,\\n hmapping, hwriteSlots, hkeyIRsInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMappingChain_singleSlot_of_slotSafety_preserves\\n hcoreKeys hinScopeKeys hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIRs hvalueIR\",\n \"n_chars\": 739,\n \"n_subproofs\": 2,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMapping_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 725,\n \"n_subproofs\": 2,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingWord_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingSlotWrite,\\n hmapping, hwriteSlots, hkeyIRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMappingWord_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue hwriteSlots hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 729,\n \"n_subproofs\": 2,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 14,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileMappingPackedSlotWrite,\\n hmapping, hpacked, hwriteSlots, hkeyIRInternal, hvalueIRInternal, Bool.not_true, bne_self_eq_false,\\n ite_false, ite_true, pure, Except.pure, bind, Except.bind]\\n simp [hfind, fieldLoadBuiltin, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue\\n hcompatValue hcompatPacked hcompatSlotWord hcompatSlotCleared\\n hpacked hwriteSlots hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 945,\n \"n_subproofs\": 2,\n \"n_tactics\": 14,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setStructMember_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 13,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkeyIRInternal := compileExprWithInternals_nil_ok hkeyIR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember,\\n CompilationModel.compileMappingSlotWrite, hmapping, hnotMapping2, hmembers, hmember,\\n hwriteSlots, hkeyIRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setStructMember_singleSlot_of_slotSafety_preserves\\n hcoreKey hinScopeKey hcoreValue hinScopeValue hmembers hmember hwriteSlots\\n hslotSafety hkeyIR hvalueIR\",\n \"n_chars\": 831,\n \"n_subproofs\": 2,\n \"n_tactics\": 13,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping2_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 13,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMapping2,\\n hmapping2, hwriteSlots, hkey1IRInternal, hkey2IRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMapping2_singleSlot_of_slotSafety_preserves\\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\",\n \"n_chars\": 848,\n \"n_subproofs\": 3,\n \"n_tactics\": 13,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 13,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetMapping2Word,\\n hmapping2, hwriteSlots, hkey1IRInternal, hkey2IRInternal, hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves\\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\\n hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\",\n \"n_chars\": 856,\n \"n_subproofs\": 3,\n \"n_tactics\": 13,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_setStructMember2_singleSlot_of_slotSafety\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 14,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases findFieldWithResolvedSlot_of_findFieldWriteSlots_singleton hwriteSlots with\\n ⟨f, hfind, _⟩\\n have hkey1IRInternal := compileExprWithInternals_nil_ok hkey1IR\\n have hkey2IRInternal := compileExprWithInternals_nil_ok hkey2IR\\n have hvalueIRInternal := compileExprWithInternals_nil_ok hvalueIR\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStructMember2,\\n hmapping2, hmembers, hmember, hwriteSlots, hkey1IRInternal, hkey2IRInternal,\\n hvalueIRInternal]\\n simp [hfind, fieldStoreBuiltin, SourceSemantics.fieldIsTransient,\\n Bind.bind, Except.bind, pure, Except.pure]\\n preserves := compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves\\n hcoreKey1 hinScopeKey1 hcoreKey2 hinScopeKey2 hcoreValue hinScopeValue\\n hmembers hmember hwriteSlots hslotSafety hkey1IR hkey2IR hvalueIR\",\n \"n_chars\": 900,\n \"n_subproofs\": 3,\n \"n_tactics\": 14,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"compiledStmtStep_ite\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 237,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcond with ⟨condIR, hcondIR⟩\\n rcases FunctionBody.compileStmtList_terminal_core_ok\\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := thenBranch)\\n hthen with ⟨thenIR, hthenIR⟩\\n rcases FunctionBody.compileStmtList_terminal_core_ok\\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := elseBranch)\\n helse with ⟨elseIR, helseIR⟩\\n have helseNonempty : elseBranch.isEmpty = false := by\\n cases elseBranch with\\n | nil => exfalso; exact FunctionBody.stmtListTerminalCore_ne_nil helse rfl\\n | cons => simp\\n let tempName :=\\n CompilationModel.pickFreshName \\\"__ite_cond\\\"\\n (scope ++ collectExprNames cond ++\\n collectStmtListNames thenBranch ++ collectStmtListNames elseBranch)\\n let compiledIR :=\\n [YulStmt.block\\n [ YulStmt.let_ tempName condIR\\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\\n , YulStmt.if_ (YulExpr.call \\\"iszero\\\" [YulExpr.ident tempName]) elseIR ]]\\n refine ⟨compiledIR, ?_⟩\\n refine\\n { compileOk := ?_\\n preserves := ?_ }\\n · show CompilationModel.compileStmt fields [] [] .calldata [] false scope []\\n (.ite cond thenBranch elseBranch) = Except.ok compiledIR\\n have hcondIRInternal := compileExprWithInternals_nil_ok hcondIR\\n unfold CompilationModel.compileStmt CompilationModel.compileStmtWithFork\\n simp [FunctionBody.compileStmtListWithFork_cancun_eq_compileStmtList,\\n hcondIRInternal, hthenIR, helseIR, Except.bind, helseNonempty]\\n simp [compiledIR, tempName, List.append_assoc, Bind.bind, Except.bind,\\n Pure.pure, Except.pure]\\n · intro runtime state extraFuel hexact hscope hbounded hruntime hslack\\n set wholeExtraFuel := extraFuel - (sizeOf compiledIR - compiledIR.length) with hWF\\n have hsizeOf_eq : sizeOf compiledIR = 1 + sizeOf (YulStmt.block\\n [ YulStmt.let_ tempName condIR\\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\\n , YulStmt.if_ (YulExpr.call \\\"iszero\\\" [YulExpr.ident tempName]) elseIR ]) + 1 := by\\n rfl\\n have hlength_eq : compiledIR.length = 1 := by rfl\\n have hwholeFuel :\\n compiledIR.length + extraFuel + 1 =\\n sizeOf compiledIR + wholeExtraFuel + 1 := by\\n rw [hWF, hsizeOf_eq, hlength_eq]\\n have : sizeOf compiledIR - compiledIR.length ≤ extraFuel := hslack\\n rw [hsizeOf_eq, hlength_eq] at this\\n omega\\n have hpresent : FunctionBody.exprBoundNamesPresent cond runtime.bindings :=\\n FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope\\n -- Extract the Nat condition value via the eval bridge\\n have heval := FunctionBody.eval_compileExpr_core_of_scope\\n hcond hexact hinScope hbounded hpresent hruntime\\n rw [hcondIR] at heval; simp [Except.toOption] at heval\\n rcases hCondIRVal : evalIRExpr state condIR with _ | condVal\\n · simp [hCondIRVal, Option.bind] at heval\\n · simp [hCondIRVal, Option.bind] at heval\\n have hCondSrc : SourceSemantics.evalExpr fields runtime cond = some condVal :=\\n heval.symm\\n have hcondEval : evalIRExpr state condIR = some condVal := hCondIRVal\\n by_cases hcondZero : condVal = 0\\n · -- Condition is zero → take else branch\\n have hBindIte :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\\n (scope := scope) (inScopeNames := scope)\\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\\n have hRuntimeIte :=\\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\\n (name := tempName) (value := condVal) hruntime\\n have hElse6 : sizeOf elseIR + 6 ≤ sizeOf compiledIR := by\\n change sizeOf elseIR + 6 ≤ sizeOf compiledIR\\n simp_wf\\n omega\\n let branchExtraFuel :=\\n sizeOf compiledIR - (sizeOf elseIR + 5) + wholeExtraFuel - 1\\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\\n (fields := fields) (runtime := runtime)\\n (state := state.setVar tempName condVal) (scope := scope)\\n (inScopeNames := scope) (stmts := elseBranch)\\n (extraFuel := branchExtraFuel)\\n helse\\n FunctionBody.scopeNamesIncluded_refl\\n hscope hBindIte hbounded hRuntimeIte with\\n ⟨elseIR', helseIR', helseSem⟩\\n rw [helseIR] at helseIR'\\n have helseEq : elseIR' = elseIR := (Except.ok.inj helseIR').symm\\n rw [show elseIR' = elseIR from helseEq] at helseSem\\n -- Fuel alignment: convert helseSem fuel to the form _ite_else expects\\n have hfuelAlign : sizeOf elseIR + branchExtraFuel + 1 =\\n sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\\n (sizeOf elseIR + 5) + wholeExtraFuel) := by\\n simp only [List.append_nil, branchExtraFuel]\\n have := hElse6\\n omega\\n have helseSem' :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmtList fields runtime elseBranch)\\n (execIRStmts (sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\\n (sizeOf elseIR + 5) + wholeExtraFuel))\\n (state.setVar tempName condVal) elseIR) := by\\n rw [← hfuelAlign]; exact helseSem\\n -- Apply _ite_else to get match for the whole ITE statement list\\n have hiteMatch :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmtList fields runtime\\n [Stmt.ite cond thenBranch elseBranch])\\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\\n state compiledIR) := by\\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_else\\n (fields := fields) (runtime := runtime) (state := state)\\n (scope := scope) (cond := cond)\\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\\n (extraFuel := wholeExtraFuel) (tempName := tempName)\\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\\n (tailIR := []) (condValue := condVal)\\n (sourceCondValue := condVal)\\n helse helseSem' hCondSrc\\n (by simp [hcondZero])\\n hcondEval hcondZero rfl\\n simp only [List.append_nil] at this\\n exact this\\n -- execStmt (.ite ...) = execStmtList elseBranch (by source semantics)\\n have hexecStmtElse : SourceSemantics.execStmt fields runtime\\n (Stmt.ite cond thenBranch elseBranch) =\\n SourceSemantics.execStmtList fields runtime elseBranch := by\\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\\n -- execStmtList [.ite ...] = execStmtList elseBranch (by terminal_ite_else_eq)\\n have hsourceEq :=\\n FunctionBody.execStmtList_terminal_core_ite_else_eq\\n (fields := fields) (runtime := runtime) (scope := scope)\\n (cond := cond) (thenBranch := thenBranch)\\n (elseBranch := elseBranch) (rest := [])\\n (condValue := condVal) helse hCondSrc\\n (by simp [hcondZero])\\n -- Rewrite hiteMatch source from execStmtList [.ite ...] to execStmtList elseBranch\\n rw [hsourceEq] at hiteMatch\\n -- Now hiteMatch : stmtResultMatchesIRExec fields\\n -- (execStmtList fields runtime elseBranch) (execIRStmts ... state compiledIR)\\n -- Convert to stmtResultMatchesIRExec about execStmt\\n have hbodyMatch :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmt fields runtime\\n (Stmt.ite cond thenBranch elseBranch))\\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\\n rw [hexecStmtElse, hwholeFuel]; exact hiteMatch\\n refine ⟨_, _, rfl, rfl, ?_⟩\\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\\n hbodyMatch\\n (by rw [hexecStmtElse]\\n exact FunctionBody.execStmtList_terminal_core_not_continue\\n (fields := fields) (runtime := runtime) (scope := scope)\\n (stmts := elseBranch) helse)\\n · -- Condition is nonzero → take then branch\\n have hBindIte :=\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\\n (scope := scope) (inScopeNames := scope)\\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\\n have hRuntimeIte :=\\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\\n (name := tempName) (value := condVal) hruntime\\n have hThen5 : sizeOf thenIR + 5 ≤ sizeOf compiledIR := by\\n change sizeOf thenIR + 5 ≤ sizeOf compiledIR\\n simp_wf\\n omega\\n let branchExtraFuel :=\\n sizeOf compiledIR - (sizeOf thenIR + 5) + wholeExtraFuel\\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\\n (fields := fields) (runtime := runtime)\\n (state := state.setVar tempName condVal) (scope := scope)\\n (inScopeNames := scope) (stmts := thenBranch)\\n (extraFuel := branchExtraFuel)\\n hthen\\n FunctionBody.scopeNamesIncluded_refl\\n hscope hBindIte hbounded hRuntimeIte with\\n ⟨thenIR', hthenIR', hthenSem⟩\\n rw [hthenIR] at hthenIR'\\n have hthenEq : thenIR' = thenIR := (Except.ok.inj hthenIR').symm\\n rw [show thenIR' = thenIR from hthenEq] at hthenSem\\n -- Fuel alignment for then branch (has +1 on both sides, so direct)\\n have hthenSem' :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmtList fields runtime thenBranch)\\n (execIRStmts (sizeOf thenIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\\n (sizeOf thenIR + 5) + wholeExtraFuel) + 1)\\n (state.setVar tempName condVal) thenIR) := by\\n simp only [List.append_nil, branchExtraFuel] at hthenSem ⊢\\n exact hthenSem\\n -- Apply _ite_then to get match for the whole ITE statement list\\n have hiteMatch :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmtList fields runtime\\n [Stmt.ite cond thenBranch elseBranch])\\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\\n state compiledIR) := by\\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_then\\n (fields := fields) (runtime := runtime) (state := state)\\n (scope := scope) (cond := cond)\\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\\n (extraFuel := wholeExtraFuel) (tempName := tempName)\\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\\n (tailIR := []) (condValue := condVal)\\n (sourceCondValue := condVal)\\n hthen hthenSem' hCondSrc\\n (by simp [hcondZero])\\n hcondEval\\n (by intro hzero; exact hcondZero hzero) rfl\\n simp only [List.append_nil] at this\\n exact this\\n -- execStmt (.ite ...) = execStmtList thenBranch (by source semantics)\\n have hexecStmtThen : SourceSemantics.execStmt fields runtime\\n (Stmt.ite cond thenBranch elseBranch) =\\n SourceSemantics.execStmtList fields runtime thenBranch := by\\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\\n -- execStmtList [.ite ...] = execStmtList thenBranch\\n have hsourceEq :=\\n FunctionBody.execStmtList_terminal_core_ite_then_eq\\n (fields := fields) (runtime := runtime) (scope := scope)\\n (cond := cond) (thenBranch := thenBranch)\\n (elseBranch := elseBranch) (rest := [])\\n (condValue := condVal) hthen hCondSrc\\n (by simp [hcondZero])\\n rw [hsourceEq] at hiteMatch\\n have hbodyMatch :\\n FunctionBody.stmtResultMatchesIRExec fields\\n (SourceSemantics.execStmt fields runtime\\n (Stmt.ite cond thenBranch elseBranch))\\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\\n rw [hexecStmtThen, hwholeFuel]; exact hiteMatch\\n refine ⟨_, _, rfl, rfl, ?_⟩\\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\\n hbodyMatch\\n (by rw [hexecStmtThen]\\n exact FunctionBody.execStmtList_terminal_core_not_continue\\n (fields := fields) (runtime := runtime) (scope := scope)\\n (stmts := thenBranch) hthen)\",\n \"n_chars\": 12831,\n \"n_subproofs\": 32,\n \"n_tactics\": 230,\n \"cyclomatic\": 8,\n \"n_automation\": 29,\n \"n_rewrites\": 20,\n \"n_structural\": 25,\n \"automation_only\": false,\n \"max_nesting\": 18\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compileExprWithInternals_nil_ok","text":"private theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\n simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\n\n","fan_in":14,"n_lines":7,"n_chars":397,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":true,"max_nesting":2}],"string":"[\n {\n \"name\": \"compileExprWithInternals_nil_ok\",\n \"text\": \"private theorem compileExprWithInternals_nil_ok\\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\\n CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\\n simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\\n\\n\",\n \"fan_in\": 14,\n \"n_lines\": 7,\n \"n_chars\": 397,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": true,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListGenericCore_singleton_iteTerminal","fan_in":0,"n_deps_direct":1,"n_deps_transitive":3,"n_lines":15,"n_chars":659,"n_subproofs":0,"n_tactics":4,"cyclomatic":2,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"stmtListGenericCore_singleton_iteTerminal\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 3,\n \"n_lines\": 15,\n \"n_chars\": 659,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 2,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n {fields : List Field}\n {scope : List String}\n {sourceResult : SourceSemantics.StmtResult}\n {irExec : IRExecResult}\n (hmatch : FunctionBody.stmtResultMatchesIRExec fields sourceResult irExec)\n (hnotContinue : ∀ next, sourceResult ≠ .continue next) :\n stmtStepMatchesIRExec fields scope sourceResult irExec := by\n cases sourceResult <;> cases irExec <;>\n simp [stmtStepMatchesIRExec, FunctionBody.stmtResultMatchesIRExec] at hmatch ⊢\n · exact False.elim (hnotContinue _ rfl)\n · exact hmatch\n · exact hmatch\n\ntheorem compiledStmtStep_ite\n {fields : List Field}\n {scope : List String}\n {cond : Expr}\n {thenBranch elseBranch : List Stmt}\n (hcond : FunctionBody.ExprCompileCore cond)\n (hinScope : FunctionBody.exprBoundNamesInScope cond scope)\n (hthen : FunctionBody.StmtListTerminalCore scope thenBranch)\n (helse : FunctionBody.StmtListTerminalCore scope elseBranch) :\n ∃ compiledIR, CompiledStmtStep fields scope (.ite cond thenBranch elseBranch) compiledIR := sorry\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\ntheorem stmtListGenericCore_singleton_iteTerminal\n {fields : List Field}\n {scope : List String}\n {cond : Expr}\n {thenBranch elseBranch : List Stmt}\n (hcond : FunctionBody.ExprCompileCore cond)\n (hinScope : FunctionBody.exprBoundNamesInScope cond scope)\n (hthen : FunctionBody.StmtListTerminalCore scope thenBranch)\n (helse : FunctionBody.StmtListTerminalCore scope elseBranch) :\n StmtListGenericCore fields scope [Stmt.ite cond thenBranch elseBranch] := by\n rcases compiledStmtStep_ite (fields := fields)\n hcond hinScope hthen helse with ⟨compiledIR, hstep⟩\n exact StmtListGenericCore.cons hstep StmtListGenericCore.nil\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\n simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nprivate theorem terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n {fields : List Field}\n {scope : List String}\n {sourceResult : SourceSemantics.StmtResult}\n {irExec : IRExecResult}\n (hmatch : FunctionBody.stmtResultMatchesIRExec fields sourceResult irExec)\n (hnotContinue : ∀ next, sourceResult ≠ .continue next) :\n stmtStepMatchesIRExec fields scope sourceResult irExec := by\n cases sourceResult <;> cases irExec <;>\n simp [stmtStepMatchesIRExec, FunctionBody.stmtResultMatchesIRExec] at hmatch ⊢\n · exact False.elim (hnotContinue _ rfl)\n · exact hmatch\n · exact hmatch\n\ntheorem compiledStmtStep_ite\n {fields : List Field}\n {scope : List String}\n {cond : Expr}\n {thenBranch elseBranch : List Stmt}\n (hcond : FunctionBody.ExprCompileCore cond)\n (hinScope : FunctionBody.exprBoundNamesInScope cond scope)\n (hthen : FunctionBody.StmtListTerminalCore scope thenBranch)\n (helse : FunctionBody.StmtListTerminalCore scope elseBranch) :\n ∃ compiledIR, CompiledStmtStep fields scope (.ite cond thenBranch elseBranch) compiledIR := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcond with ⟨condIR, hcondIR⟩\n rcases FunctionBody.compileStmtList_terminal_core_ok\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := thenBranch)\n hthen with ⟨thenIR, hthenIR⟩\n rcases FunctionBody.compileStmtList_terminal_core_ok\n (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := elseBranch)\n helse with ⟨elseIR, helseIR⟩\n have helseNonempty : elseBranch.isEmpty = false := by\n cases elseBranch with\n | nil => exfalso; exact FunctionBody.stmtListTerminalCore_ne_nil helse rfl\n | cons => simp\n let tempName :=\n CompilationModel.pickFreshName \"__ite_cond\"\n (scope ++ collectExprNames cond ++\n collectStmtListNames thenBranch ++ collectStmtListNames elseBranch)\n let compiledIR :=\n [YulStmt.block\n [ YulStmt.let_ tempName condIR\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\n , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]]\n refine ⟨compiledIR, ?_⟩\n refine\n { compileOk := ?_\n preserves := ?_ }\n · show CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (.ite cond thenBranch elseBranch) = Except.ok compiledIR\n have hcondIRInternal := compileExprWithInternals_nil_ok hcondIR\n unfold CompilationModel.compileStmt CompilationModel.compileStmtWithFork\n simp [FunctionBody.compileStmtListWithFork_cancun_eq_compileStmtList,\n hcondIRInternal, hthenIR, helseIR, Except.bind, helseNonempty]\n simp [compiledIR, tempName, List.append_assoc, Bind.bind, Except.bind,\n Pure.pure, Except.pure]\n · intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n set wholeExtraFuel := extraFuel - (sizeOf compiledIR - compiledIR.length) with hWF\n have hsizeOf_eq : sizeOf compiledIR = 1 + sizeOf (YulStmt.block\n [ YulStmt.let_ tempName condIR\n , YulStmt.if_ (YulExpr.ident tempName) thenIR\n , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]) + 1 := by\n rfl\n have hlength_eq : compiledIR.length = 1 := by rfl\n have hwholeFuel :\n compiledIR.length + extraFuel + 1 =\n sizeOf compiledIR + wholeExtraFuel + 1 := by\n rw [hWF, hsizeOf_eq, hlength_eq]\n have : sizeOf compiledIR - compiledIR.length ≤ extraFuel := hslack\n rw [hsizeOf_eq, hlength_eq] at this\n omega\n have hpresent : FunctionBody.exprBoundNamesPresent cond runtime.bindings :=\n FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope\n -- Extract the Nat condition value via the eval bridge\n have heval := FunctionBody.eval_compileExpr_core_of_scope\n hcond hexact hinScope hbounded hpresent hruntime\n rw [hcondIR] at heval; simp [Except.toOption] at heval\n rcases hCondIRVal : evalIRExpr state condIR with _ | condVal\n · simp [hCondIRVal, Option.bind] at heval\n · simp [hCondIRVal, Option.bind] at heval\n have hCondSrc : SourceSemantics.evalExpr fields runtime cond = some condVal :=\n heval.symm\n have hcondEval : evalIRExpr state condIR = some condVal := hCondIRVal\n by_cases hcondZero : condVal = 0\n · -- Condition is zero → take else branch\n have hBindIte :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n (scope := scope) (inScopeNames := scope)\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n have hRuntimeIte :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := tempName) (value := condVal) hruntime\n have hElse6 : sizeOf elseIR + 6 ≤ sizeOf compiledIR := by\n change sizeOf elseIR + 6 ≤ sizeOf compiledIR\n simp_wf\n omega\n let branchExtraFuel :=\n sizeOf compiledIR - (sizeOf elseIR + 5) + wholeExtraFuel - 1\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n (fields := fields) (runtime := runtime)\n (state := state.setVar tempName condVal) (scope := scope)\n (inScopeNames := scope) (stmts := elseBranch)\n (extraFuel := branchExtraFuel)\n helse\n FunctionBody.scopeNamesIncluded_refl\n hscope hBindIte hbounded hRuntimeIte with\n ⟨elseIR', helseIR', helseSem⟩\n rw [helseIR] at helseIR'\n have helseEq : elseIR' = elseIR := (Except.ok.inj helseIR').symm\n rw [show elseIR' = elseIR from helseEq] at helseSem\n -- Fuel alignment: convert helseSem fuel to the form _ite_else expects\n have hfuelAlign : sizeOf elseIR + branchExtraFuel + 1 =\n sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf elseIR + 5) + wholeExtraFuel) := by\n simp only [List.append_nil, branchExtraFuel]\n have := hElse6\n omega\n have helseSem' :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime elseBranch)\n (execIRStmts (sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf elseIR + 5) + wholeExtraFuel))\n (state.setVar tempName condVal) elseIR) := by\n rw [← hfuelAlign]; exact helseSem\n -- Apply _ite_else to get match for the whole ITE statement list\n have hiteMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime\n [Stmt.ite cond thenBranch elseBranch])\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n state compiledIR) := by\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_else\n (fields := fields) (runtime := runtime) (state := state)\n (scope := scope) (cond := cond)\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n (extraFuel := wholeExtraFuel) (tempName := tempName)\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n (tailIR := []) (condValue := condVal)\n (sourceCondValue := condVal)\n helse helseSem' hCondSrc\n (by simp [hcondZero])\n hcondEval hcondZero rfl\n simp only [List.append_nil] at this\n exact this\n -- execStmt (.ite ...) = execStmtList elseBranch (by source semantics)\n have hexecStmtElse : SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch) =\n SourceSemantics.execStmtList fields runtime elseBranch := by\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n -- execStmtList [.ite ...] = execStmtList elseBranch (by terminal_ite_else_eq)\n have hsourceEq :=\n FunctionBody.execStmtList_terminal_core_ite_else_eq\n (fields := fields) (runtime := runtime) (scope := scope)\n (cond := cond) (thenBranch := thenBranch)\n (elseBranch := elseBranch) (rest := [])\n (condValue := condVal) helse hCondSrc\n (by simp [hcondZero])\n -- Rewrite hiteMatch source from execStmtList [.ite ...] to execStmtList elseBranch\n rw [hsourceEq] at hiteMatch\n -- Now hiteMatch : stmtResultMatchesIRExec fields\n -- (execStmtList fields runtime elseBranch) (execIRStmts ... state compiledIR)\n -- Convert to stmtResultMatchesIRExec about execStmt\n have hbodyMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch))\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n rw [hexecStmtElse, hwholeFuel]; exact hiteMatch\n refine ⟨_, _, rfl, rfl, ?_⟩\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n hbodyMatch\n (by rw [hexecStmtElse]\n exact FunctionBody.execStmtList_terminal_core_not_continue\n (fields := fields) (runtime := runtime) (scope := scope)\n (stmts := elseBranch) helse)\n · -- Condition is nonzero → take then branch\n have hBindIte :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n (scope := scope) (inScopeNames := scope)\n (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n have hRuntimeIte :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := tempName) (value := condVal) hruntime\n have hThen5 : sizeOf thenIR + 5 ≤ sizeOf compiledIR := by\n change sizeOf thenIR + 5 ≤ sizeOf compiledIR\n simp_wf\n omega\n let branchExtraFuel :=\n sizeOf compiledIR - (sizeOf thenIR + 5) + wholeExtraFuel\n rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n (fields := fields) (runtime := runtime)\n (state := state.setVar tempName condVal) (scope := scope)\n (inScopeNames := scope) (stmts := thenBranch)\n (extraFuel := branchExtraFuel)\n hthen\n FunctionBody.scopeNamesIncluded_refl\n hscope hBindIte hbounded hRuntimeIte with\n ⟨thenIR', hthenIR', hthenSem⟩\n rw [hthenIR] at hthenIR'\n have hthenEq : thenIR' = thenIR := (Except.ok.inj hthenIR').symm\n rw [show thenIR' = thenIR from hthenEq] at hthenSem\n -- Fuel alignment for then branch (has +1 on both sides, so direct)\n have hthenSem' :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime thenBranch)\n (execIRStmts (sizeOf thenIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n (sizeOf thenIR + 5) + wholeExtraFuel) + 1)\n (state.setVar tempName condVal) thenIR) := by\n simp only [List.append_nil, branchExtraFuel] at hthenSem ⊢\n exact hthenSem\n -- Apply _ite_then to get match for the whole ITE statement list\n have hiteMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmtList fields runtime\n [Stmt.ite cond thenBranch elseBranch])\n (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n state compiledIR) := by\n have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_then\n (fields := fields) (runtime := runtime) (state := state)\n (scope := scope) (cond := cond)\n (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n (extraFuel := wholeExtraFuel) (tempName := tempName)\n (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n (tailIR := []) (condValue := condVal)\n (sourceCondValue := condVal)\n hthen hthenSem' hCondSrc\n (by simp [hcondZero])\n hcondEval\n (by intro hzero; exact hcondZero hzero) rfl\n simp only [List.append_nil] at this\n exact this\n -- execStmt (.ite ...) = execStmtList thenBranch (by source semantics)\n have hexecStmtThen : SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch) =\n SourceSemantics.execStmtList fields runtime thenBranch := by\n simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n -- execStmtList [.ite ...] = execStmtList thenBranch\n have hsourceEq :=\n FunctionBody.execStmtList_terminal_core_ite_then_eq\n (fields := fields) (runtime := runtime) (scope := scope)\n (cond := cond) (thenBranch := thenBranch)\n (elseBranch := elseBranch) (rest := [])\n (condValue := condVal) hthen hCondSrc\n (by simp [hcondZero])\n rw [hsourceEq] at hiteMatch\n have hbodyMatch :\n FunctionBody.stmtResultMatchesIRExec fields\n (SourceSemantics.execStmt fields runtime\n (Stmt.ite cond thenBranch elseBranch))\n (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n rw [hexecStmtThen, hwholeFuel]; exact hiteMatch\n refine ⟨_, _, rfl, rfl, ?_⟩\n exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n hbodyMatch\n (by rw [hexecStmtThen]\n exact FunctionBody.execStmtList_terminal_core_not_continue\n (fields := fields) (runtime := runtime) (scope := scope)\n (stmts := thenBranch) hthen)\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\ntheorem stmtListGenericCore_singleton_iteTerminal\n {fields : List Field}\n {scope : List String}\n {cond : Expr}\n {thenBranch elseBranch : List Stmt}\n (hcond : FunctionBody.ExprCompileCore cond)\n (hinScope : FunctionBody.exprBoundNamesInScope cond scope)\n (hthen : FunctionBody.StmtListTerminalCore scope thenBranch)\n (helse : FunctionBody.StmtListTerminalCore scope elseBranch) :\n StmtListGenericCore fields scope [Stmt.ite cond thenBranch elseBranch] := by\n rcases compiledStmtStep_ite (fields := fields)\n hcond hinScope hthen helse with ⟨compiledIR, hstep⟩\n exact StmtListGenericCore.cons hstep StmtListGenericCore.nil\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -12,6 +12,12 @@\n \n attribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n \n+private theorem compileExprWithInternals_nil_ok\n+ {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n+ (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n+ CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by\n+ simpa [CompilationModel.compileExprWithInternals_nil_eq] using h\n+\n set_option maxHeartbeats 800000 in\n private theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n@@ -1948,7 +1954,243 @@\n (hinScope : FunctionBody.exprBoundNamesInScope cond scope)\n (hthen : FunctionBody.StmtListTerminalCore scope thenBranch)\n (helse : FunctionBody.StmtListTerminalCore scope elseBranch) :\n- ∃ compiledIR, CompiledStmtStep fields scope (.ite cond thenBranch elseBranch) compiledIR := sorry\n+ ∃ compiledIR, CompiledStmtStep fields scope (.ite cond thenBranch elseBranch) compiledIR := by\n+ rcases FunctionBody.compileExpr_core_ok (fields := fields) hcond with ⟨condIR, hcondIR⟩\n+ rcases FunctionBody.compileStmtList_terminal_core_ok\n+ (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := thenBranch)\n+ hthen with ⟨thenIR, hthenIR⟩\n+ rcases FunctionBody.compileStmtList_terminal_core_ok\n+ (fields := fields) (scope := scope) (inScopeNames := scope) (stmts := elseBranch)\n+ helse with ⟨elseIR, helseIR⟩\n+ have helseNonempty : elseBranch.isEmpty = false := by\n+ cases elseBranch with\n+ | nil => exfalso; exact FunctionBody.stmtListTerminalCore_ne_nil helse rfl\n+ | cons => simp\n+ let tempName :=\n+ CompilationModel.pickFreshName \"__ite_cond\"\n+ (scope ++ collectExprNames cond ++\n+ collectStmtListNames thenBranch ++ collectStmtListNames elseBranch)\n+ let compiledIR :=\n+ [YulStmt.block\n+ [ YulStmt.let_ tempName condIR\n+ , YulStmt.if_ (YulExpr.ident tempName) thenIR\n+ , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]]\n+ refine ⟨compiledIR, ?_⟩\n+ refine\n+ { compileOk := ?_\n+ preserves := ?_ }\n+ · show CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n+ (.ite cond thenBranch elseBranch) = Except.ok compiledIR\n+ have hcondIRInternal := compileExprWithInternals_nil_ok hcondIR\n+ unfold CompilationModel.compileStmt CompilationModel.compileStmtWithFork\n+ simp [FunctionBody.compileStmtListWithFork_cancun_eq_compileStmtList,\n+ hcondIRInternal, hthenIR, helseIR, Except.bind, helseNonempty]\n+ simp [compiledIR, tempName, List.append_assoc, Bind.bind, Except.bind,\n+ Pure.pure, Except.pure]\n+ · intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n+ set wholeExtraFuel := extraFuel - (sizeOf compiledIR - compiledIR.length) with hWF\n+ have hsizeOf_eq : sizeOf compiledIR = 1 + sizeOf (YulStmt.block\n+ [ YulStmt.let_ tempName condIR\n+ , YulStmt.if_ (YulExpr.ident tempName) thenIR\n+ , YulStmt.if_ (YulExpr.call \"iszero\" [YulExpr.ident tempName]) elseIR ]) + 1 := by\n+ rfl\n+ have hlength_eq : compiledIR.length = 1 := by rfl\n+ have hwholeFuel :\n+ compiledIR.length + extraFuel + 1 =\n+ sizeOf compiledIR + wholeExtraFuel + 1 := by\n+ rw [hWF, hsizeOf_eq, hlength_eq]\n+ have : sizeOf compiledIR - compiledIR.length ≤ extraFuel := hslack\n+ rw [hsizeOf_eq, hlength_eq] at this\n+ omega\n+ have hpresent : FunctionBody.exprBoundNamesPresent cond runtime.bindings :=\n+ FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope\n+ -- Extract the Nat condition value via the eval bridge\n+ have heval := FunctionBody.eval_compileExpr_core_of_scope\n+ hcond hexact hinScope hbounded hpresent hruntime\n+ rw [hcondIR] at heval; simp [Except.toOption] at heval\n+ rcases hCondIRVal : evalIRExpr state condIR with _ | condVal\n+ · simp [hCondIRVal, Option.bind] at heval\n+ · simp [hCondIRVal, Option.bind] at heval\n+ have hCondSrc : SourceSemantics.evalExpr fields runtime cond = some condVal :=\n+ heval.symm\n+ have hcondEval : evalIRExpr state condIR = some condVal := hCondIRVal\n+ by_cases hcondZero : condVal = 0\n+ · -- Condition is zero → take else branch\n+ have hBindIte :=\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n+ (scope := scope) (inScopeNames := scope)\n+ (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n+ (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n+ have hRuntimeIte :=\n+ FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n+ (name := tempName) (value := condVal) hruntime\n+ have hElse6 : sizeOf elseIR + 6 ≤ sizeOf compiledIR := by\n+ change sizeOf elseIR + 6 ≤ sizeOf compiledIR\n+ simp_wf\n+ omega\n+ let branchExtraFuel :=\n+ sizeOf compiledIR - (sizeOf elseIR + 5) + wholeExtraFuel - 1\n+ rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n+ (fields := fields) (runtime := runtime)\n+ (state := state.setVar tempName condVal) (scope := scope)\n+ (inScopeNames := scope) (stmts := elseBranch)\n+ (extraFuel := branchExtraFuel)\n+ helse\n+ FunctionBody.scopeNamesIncluded_refl\n+ hscope hBindIte hbounded hRuntimeIte with\n+ ⟨elseIR', helseIR', helseSem⟩\n+ rw [helseIR] at helseIR'\n+ have helseEq : elseIR' = elseIR := (Except.ok.inj helseIR').symm\n+ rw [show elseIR' = elseIR from helseEq] at helseSem\n+ -- Fuel alignment: convert helseSem fuel to the form _ite_else expects\n+ have hfuelAlign : sizeOf elseIR + branchExtraFuel + 1 =\n+ sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n+ (sizeOf elseIR + 5) + wholeExtraFuel) := by\n+ simp only [List.append_nil, branchExtraFuel]\n+ have := hElse6\n+ omega\n+ have helseSem' :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmtList fields runtime elseBranch)\n+ (execIRStmts (sizeOf elseIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n+ (sizeOf elseIR + 5) + wholeExtraFuel))\n+ (state.setVar tempName condVal) elseIR) := by\n+ rw [← hfuelAlign]; exact helseSem\n+ -- Apply _ite_else to get match for the whole ITE statement list\n+ have hiteMatch :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmtList fields runtime\n+ [Stmt.ite cond thenBranch elseBranch])\n+ (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n+ state compiledIR) := by\n+ have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_else\n+ (fields := fields) (runtime := runtime) (state := state)\n+ (scope := scope) (cond := cond)\n+ (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n+ (extraFuel := wholeExtraFuel) (tempName := tempName)\n+ (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n+ (tailIR := []) (condValue := condVal)\n+ (sourceCondValue := condVal)\n+ helse helseSem' hCondSrc\n+ (by simp [hcondZero])\n+ hcondEval hcondZero rfl\n+ simp only [List.append_nil] at this\n+ exact this\n+ -- execStmt (.ite ...) = execStmtList elseBranch (by source semantics)\n+ have hexecStmtElse : SourceSemantics.execStmt fields runtime\n+ (Stmt.ite cond thenBranch elseBranch) =\n+ SourceSemantics.execStmtList fields runtime elseBranch := by\n+ simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n+ -- execStmtList [.ite ...] = execStmtList elseBranch (by terminal_ite_else_eq)\n+ have hsourceEq :=\n+ FunctionBody.execStmtList_terminal_core_ite_else_eq\n+ (fields := fields) (runtime := runtime) (scope := scope)\n+ (cond := cond) (thenBranch := thenBranch)\n+ (elseBranch := elseBranch) (rest := [])\n+ (condValue := condVal) helse hCondSrc\n+ (by simp [hcondZero])\n+ -- Rewrite hiteMatch source from execStmtList [.ite ...] to execStmtList elseBranch\n+ rw [hsourceEq] at hiteMatch\n+ -- Now hiteMatch : stmtResultMatchesIRExec fields\n+ -- (execStmtList fields runtime elseBranch) (execIRStmts ... state compiledIR)\n+ -- Convert to stmtResultMatchesIRExec about execStmt\n+ have hbodyMatch :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmt fields runtime\n+ (Stmt.ite cond thenBranch elseBranch))\n+ (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n+ rw [hexecStmtElse, hwholeFuel]; exact hiteMatch\n+ refine ⟨_, _, rfl, rfl, ?_⟩\n+ exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n+ hbodyMatch\n+ (by rw [hexecStmtElse]\n+ exact FunctionBody.execStmtList_terminal_core_not_continue\n+ (fields := fields) (runtime := runtime) (scope := scope)\n+ (stmts := elseBranch) helse)\n+ · -- Condition is nonzero → take then branch\n+ have hBindIte :=\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope_setCompiledTerminalIteTemp_irrelevant\n+ (scope := scope) (inScopeNames := scope)\n+ (cond := cond) (thenBranch := thenBranch) (elseBranch := elseBranch)\n+ (value := condVal) hexact FunctionBody.scopeNamesIncluded_refl\n+ have hRuntimeIte :=\n+ FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n+ (name := tempName) (value := condVal) hruntime\n+ have hThen5 : sizeOf thenIR + 5 ≤ sizeOf compiledIR := by\n+ change sizeOf thenIR + 5 ≤ sizeOf compiledIR\n+ simp_wf\n+ omega\n+ let branchExtraFuel :=\n+ sizeOf compiledIR - (sizeOf thenIR + 5) + wholeExtraFuel\n+ rcases FunctionBody.exec_compileStmtList_terminal_core_sizeOf_extraFuel\n+ (fields := fields) (runtime := runtime)\n+ (state := state.setVar tempName condVal) (scope := scope)\n+ (inScopeNames := scope) (stmts := thenBranch)\n+ (extraFuel := branchExtraFuel)\n+ hthen\n+ FunctionBody.scopeNamesIncluded_refl\n+ hscope hBindIte hbounded hRuntimeIte with\n+ ⟨thenIR', hthenIR', hthenSem⟩\n+ rw [hthenIR] at hthenIR'\n+ have hthenEq : thenIR' = thenIR := (Except.ok.inj hthenIR').symm\n+ rw [show thenIR' = thenIR from hthenEq] at hthenSem\n+ -- Fuel alignment for then branch (has +1 on both sides, so direct)\n+ have hthenSem' :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmtList fields runtime thenBranch)\n+ (execIRStmts (sizeOf thenIR + (sizeOf (compiledIR ++ ([] : List YulStmt)) -\n+ (sizeOf thenIR + 5) + wholeExtraFuel) + 1)\n+ (state.setVar tempName condVal) thenIR) := by\n+ simp only [List.append_nil, branchExtraFuel] at hthenSem ⊢\n+ exact hthenSem\n+ -- Apply _ite_then to get match for the whole ITE statement list\n+ have hiteMatch :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmtList fields runtime\n+ [Stmt.ite cond thenBranch elseBranch])\n+ (execIRStmts (sizeOf compiledIR + wholeExtraFuel + 1)\n+ state compiledIR) := by\n+ have := FunctionBody.stmtResultMatchesIRExec_compiled_terminal_ite_then\n+ (fields := fields) (runtime := runtime) (state := state)\n+ (scope := scope) (cond := cond)\n+ (thenBranch := thenBranch) (elseBranch := elseBranch) (rest := [])\n+ (extraFuel := wholeExtraFuel) (tempName := tempName)\n+ (condIR := condIR) (thenIR := thenIR) (elseIR := elseIR)\n+ (tailIR := []) (condValue := condVal)\n+ (sourceCondValue := condVal)\n+ hthen hthenSem' hCondSrc\n+ (by simp [hcondZero])\n+ hcondEval\n+ (by intro hzero; exact hcondZero hzero) rfl\n+ simp only [List.append_nil] at this\n+ exact this\n+ -- execStmt (.ite ...) = execStmtList thenBranch (by source semantics)\n+ have hexecStmtThen : SourceSemantics.execStmt fields runtime\n+ (Stmt.ite cond thenBranch elseBranch) =\n+ SourceSemantics.execStmtList fields runtime thenBranch := by\n+ simp [SourceSemantics.execStmt, hCondSrc, hcondZero]\n+ -- execStmtList [.ite ...] = execStmtList thenBranch\n+ have hsourceEq :=\n+ FunctionBody.execStmtList_terminal_core_ite_then_eq\n+ (fields := fields) (runtime := runtime) (scope := scope)\n+ (cond := cond) (thenBranch := thenBranch)\n+ (elseBranch := elseBranch) (rest := [])\n+ (condValue := condVal) hthen hCondSrc\n+ (by simp [hcondZero])\n+ rw [hsourceEq] at hiteMatch\n+ have hbodyMatch :\n+ FunctionBody.stmtResultMatchesIRExec fields\n+ (SourceSemantics.execStmt fields runtime\n+ (Stmt.ite cond thenBranch elseBranch))\n+ (execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR) := by\n+ rw [hexecStmtThen, hwholeFuel]; exact hiteMatch\n+ refine ⟨_, _, rfl, rfl, ?_⟩\n+ exact terminal_stmtResultMatchesIRExec_implies_stmtStepMatchesIRExec\n+ hbodyMatch\n+ (by rw [hexecStmtThen]\n+ exact FunctionBody.execStmtList_terminal_core_not_continue\n+ (fields := fields) (runtime := runtime) (scope := scope)\n+ (stmts := thenBranch) hthen)\n \n set_option maxHeartbeats 800000 in\n private theorem compiledStmtStep_letStorageField\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21344,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_71"},"challenge_id":{"kind":"string","value":"cc93062013058d97"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":71,"string":"71"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked","depth":1,"n_commands":0,"n_lines":35,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone","n_chars":1537,"n_subproofs":6,"n_tactics":34,"cyclomatic":5,"n_automation":13,"n_rewrites":3,"n_structural":10,"automation_only":false,"max_nesting":14}],"string":"[\n {\n \"theorem_name\": \"firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 35,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction current generalizing seen with\\n | nil =>\\n simp at hcurrent\\n | cons entry rest ih =>\\n simp at hcurrent\\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\\n have hunpackedRest :\\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\\n intro packed hmem\\n exact hunpacked packed (by simp [hmem])\\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\\n obtain ⟨e1, e21, e22⟩ := entry\\n simp at hpnone\\n subst hpnone\\n -- Now entry = (e1, e21, none)\\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\\n · -- slot = e1\\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\\n simp only [firstInFieldConflictCopy]\\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\\n · exact absurd hf hfindSeen\\n · simp\\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\\n intro hnone\\n simp only [firstInFieldConflictCopy] at hnone\\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\\n · rw [hfind] at hnone\\n simp at hnone\\n have hseen' :\\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\\n simp [hseen]\\n exact (ih hseen' hrest' hunpackedRest) hnone\\n · rw [hfind] at hnone; simp at hnone\",\n \"n_chars\": 1537,\n \"n_subproofs\": 6,\n \"n_tactics\": 34,\n \"cyclomatic\": 5,\n \"n_automation\": 13,\n \"n_rewrites\": 3,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 14\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"list_findSlotPackedNone_ne_none","text":"private theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\n","fan_in":1,"n_lines":27,"n_chars":973,"n_subproofs":2,"n_tactics":21,"cyclomatic":5,"n_automation":9,"n_rewrites":3,"n_structural":6,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"list_findSlotPackedNone_ne_none\",\n \"text\": \"private theorem list_findSlotPackedNone_ne_none\\n {seen : List (Nat × String × Option PackedBits)}\\n {slot : Nat}\\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\\n induction seen with\\n | nil => simp at hmem\\n | cons entry rest ih =>\\n simp at hmem\\n by_cases hEq : entry.1 = slot\\n · subst hEq\\n simp only [List.find?]\\n cases entry.2.2 with\\n | none => simp [packedSlotsConflict]\\n | some _ => simp [packedSlotsConflict]\\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\\n · exact absurd rfl hEq\\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\\n have hih := ih hrest\\n change List.find? _ (entry :: rest) ≠ none\\n rw [List.find?_cons]\\n split\\n · simp\\n · exact hih\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 27,\n \"n_chars\": 973,\n \"n_subproofs\": 2,\n \"n_tactics\": 21,\n \"cyclomatic\": 5,\n \"n_automation\": 9,\n \"n_rewrites\": 3,\n \"n_structural\": 6,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListGenericCore_singleton_setStorage_singleSlot","fan_in":1,"n_deps_direct":2,"n_deps_transitive":29,"n_lines":34,"n_chars":1288,"n_subproofs":0,"n_tactics":21,"cyclomatic":3,"n_automation":7,"n_rewrites":0,"n_structural":4,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"stmtListGenericCore_singleton_setStorage_singleSlot\",\n \"fan_in\": 1,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 29,\n \"n_lines\": 34,\n \"n_chars\": 1288,\n \"n_subproofs\": 0,\n \"n_tactics\": 21,\n \"cyclomatic\": 3,\n \"n_automation\": 7,\n \"n_rewrites\": 0,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":23,"string":"23"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := sorry\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\ntheorem stmtListGenericCore_singleton_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {slot : Nat}\n {value : Expr}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorage fieldName value] := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcore with\n ⟨valueIR, hvalueIR⟩\n exact StmtListGenericCore.cons\n (compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind)\n (halias := by rfl)\n (hunpacked := by rfl)\n (hnoConflict := hnoConflict)\n (hnotAddr := by rfl)\n (hnotDyn := by rfl)\n (hnotTransient := by rfl)\n (hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl)\n (hNotAdt := by\n intro name maxFields hty\n cases hty)\n (hvalueIR := hvalueIR))\n StmtListGenericCore.nil\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\ntheorem stmtListGenericCore_singleton_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {slot : Nat}\n {value : Expr}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorage fieldName value] := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcore with\n ⟨valueIR, hvalueIR⟩\n exact StmtListGenericCore.cons\n (compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind)\n (halias := by rfl)\n (hunpacked := by rfl)\n (hnoConflict := hnoConflict)\n (hnotAddr := by rfl)\n (hnotDyn := by rfl)\n (hnotTransient := by rfl)\n (hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl)\n (hNotAdt := by\n intro name maxFields hty\n cases hty)\n (hvalueIR := hvalueIR))\n StmtListGenericCore.nil\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -397,13 +397,73 @@\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n \n+private theorem list_findSlotPackedNone_ne_none\n+ {seen : List (Nat × String × Option PackedBits)}\n+ {slot : Nat}\n+ (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n+ (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n+ induction seen with\n+ | nil => simp at hmem\n+ | cons entry rest ih =>\n+ simp at hmem\n+ by_cases hEq : entry.1 = slot\n+ · subst hEq\n+ simp only [List.find?]\n+ cases entry.2.2 with\n+ | none => simp [packedSlotsConflict]\n+ | some _ => simp [packedSlotsConflict]\n+ · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n+ rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n+ · exact absurd rfl hEq\n+ · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n+ have hih := ih hrest\n+ change List.find? _ (entry :: rest) ≠ none\n+ rw [List.find?_cons]\n+ split\n+ · simp\n+ · exact hih\n+\n private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n- firstInFieldConflictCopy seen current ≠ none := sorry\n+ firstInFieldConflictCopy seen current ≠ none := by\n+ induction current generalizing seen with\n+ | nil =>\n+ simp at hcurrent\n+ | cons entry rest ih =>\n+ simp at hcurrent\n+ have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n+ have hunpackedRest :\n+ ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n+ intro packed hmem\n+ exact hunpacked packed (by simp [hmem])\n+ -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n+ obtain ⟨e1, e21, e22⟩ := entry\n+ simp at hpnone\n+ subst hpnone\n+ -- Now entry = (e1, e21, none)\n+ rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n+ · -- slot = e1\n+ have hfindSeen := list_findSlotPackedNone_ne_none hseen\n+ simp only [firstInFieldConflictCopy]\n+ cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n+ · exact absurd hf hfindSeen\n+ · simp\n+ · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n+ List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n+ intro hnone\n+ simp only [firstInFieldConflictCopy] at hnone\n+ cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n+ · rw [hfind] at hnone\n+ simp at hnone\n+ have hseen' :\n+ slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n+ simp [hseen]\n+ exact (ih hseen' hrest' hunpackedRest) hnone\n+ · rw [hfind] at hnone; simp at hnone\n \n private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21345,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_72"},"challenge_id":{"kind":"string","value":"540728b25bf44833"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":72,"string":"72"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked","depth":1,"n_commands":0,"n_lines":35,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone","n_chars":1537,"n_subproofs":6,"n_tactics":34,"cyclomatic":5,"n_automation":13,"n_rewrites":3,"n_structural":10,"automation_only":false,"max_nesting":14}],"string":"[\n {\n \"theorem_name\": \"firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 35,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction current generalizing seen with\\n | nil =>\\n simp at hcurrent\\n | cons entry rest ih =>\\n simp at hcurrent\\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\\n have hunpackedRest :\\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\\n intro packed hmem\\n exact hunpacked packed (by simp [hmem])\\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\\n obtain ⟨e1, e21, e22⟩ := entry\\n simp at hpnone\\n subst hpnone\\n -- Now entry = (e1, e21, none)\\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\\n · -- slot = e1\\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\\n simp only [firstInFieldConflictCopy]\\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\\n · exact absurd hf hfindSeen\\n · simp\\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\\n intro hnone\\n simp only [firstInFieldConflictCopy] at hnone\\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\\n · rw [hfind] at hnone\\n simp at hnone\\n have hseen' :\\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\\n simp [hseen]\\n exact (ih hseen' hrest' hunpackedRest) hnone\\n · rw [hfind] at hnone; simp at hnone\",\n \"n_chars\": 1537,\n \"n_subproofs\": 6,\n \"n_tactics\": 34,\n \"cyclomatic\": 5,\n \"n_automation\": 13,\n \"n_rewrites\": 3,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 14\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"list_findSlotPackedNone_ne_none","text":"private theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\n","fan_in":1,"n_lines":27,"n_chars":973,"n_subproofs":2,"n_tactics":21,"cyclomatic":5,"n_automation":9,"n_rewrites":3,"n_structural":6,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"list_findSlotPackedNone_ne_none\",\n \"text\": \"private theorem list_findSlotPackedNone_ne_none\\n {seen : List (Nat × String × Option PackedBits)}\\n {slot : Nat}\\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\\n induction seen with\\n | nil => simp at hmem\\n | cons entry rest ih =>\\n simp at hmem\\n by_cases hEq : entry.1 = slot\\n · subst hEq\\n simp only [List.find?]\\n cases entry.2.2 with\\n | none => simp [packedSlotsConflict]\\n | some _ => simp [packedSlotsConflict]\\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\\n · exact absurd rfl hEq\\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\\n have hih := ih hrest\\n change List.find? _ (entry :: rest) ≠ none\\n rw [List.find?_cons]\\n split\\n · simp\\n · exact hih\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 27,\n \"n_chars\": 973,\n \"n_subproofs\": 2,\n \"n_tactics\": 21,\n \"cyclomatic\": 5,\n \"n_automation\": 9,\n \"n_rewrites\": 3,\n \"n_structural\": 6,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListGenericCore_singleton_setStorageAddr_singleSlot","fan_in":1,"n_deps_direct":2,"n_deps_transitive":29,"n_lines":25,"n_chars":1011,"n_subproofs":0,"n_tactics":12,"cyclomatic":2,"n_automation":1,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"stmtListGenericCore_singleton_setStorageAddr_singleSlot\",\n \"fan_in\": 1,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 29,\n \"n_lines\": 25,\n \"n_chars\": 1011,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":23,"string":"23"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := sorry\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Compiler.Constants.evmModulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeAddressSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot\n (value &&& Compiler.Constants.addressMask) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' haddr hnotDyn]\n simp [SourceSemantics.writeAddressSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS,\n Verity.wordToAddress, Verity.Core.Address.ofNat, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Address.modulus, Compiler.Constants.addressMask]\n rw [Nat.mod_eq_of_lt hvalue]\n refine congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat ?_\n simpa [Compiler.Constants.addressMask, Verity.Core.Address.modulus] using\n (Nat.and_two_pow_sub_one_eq_mod (n := 160) value)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n symm\n refine congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat ?_\n have hneqNat := IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq\n have hneqNat' : query.toNat ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneqNat\n apply SourceSemantics.encodeStorageAt_congr\n · simp [SourceSemantics.writeAddressSlots]\n · simp [SourceSemantics.writeAddressSlots, SourceSemantics.wordNormalize, hneqNat']\n · simp [SourceSemantics.writeAddressSlots]\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem compiledStmtStep_setStorageAddr_singleSlot_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ runtime state extraFuel,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] -\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime (.setStorageAddr fieldName value) = sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] =\n irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setStorageAddr fieldName value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR :=\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])]\n have hresolvedSlot : findResolvedFieldAtSlotCopy fields slot =\n some { name := fieldName, ty := FieldType.address } :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots (by rfl)\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n have hMaskedEvalRaw :\n evalIRExpr state\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]) =\n some ((valueNat % Compiler.Constants.evmModulus) &&&\n (Compiler.Constants.addressMask % Compiler.Constants.evmModulus)) := by\n simpa using FunctionBody.evalIRExpr_and_of_eval\n (state := state)\n (lhs := valueIR)\n (rhs := YulExpr.hex Compiler.Constants.addressMask)\n (b := Compiler.Constants.addressMask)\n hIRValue\n (by simp [evalIRExpr, Compiler.Constants.addressMask])\n have hMaskedEval :\n evalIRExpr state\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]) =\n some (valueNat &&& Compiler.Constants.addressMask) := by\n simpa [Nat.mod_eq_of_lt hvalueLt, Compiler.Constants.addressMask] using hMaskedEvalRaw\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot\n (valueNat &&& Compiler.Constants.addressMask) }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorageAddr fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeAddressFieldSlots,\n hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask])\n (valueNat &&& Compiler.Constants.addressMask)\n hMaskedEval\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorageAddr fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n (state := state) (slot := slot)\n (value := valueNat &&& Compiler.Constants.addressMask) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressSlot hruntime hresolvedSlot (by rfl) (by rfl) hvalueLt,\n hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorageAddr_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorageAddr fieldName value)\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] where\n compileOk := by\n have hNotMapping : isMapping fields fieldName = false :=\n isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, hvalueIR]\n preserves := compiledStmtStep_setStorageAddr_singleSlot_preserves\n hcore hinScope hfind hwriteSlots hnoConflict hvalueIR\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nprivate theorem stmtListGenericCore_singleton_setStorageAddr_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {slot : Nat}\n {value : Expr}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorageAddr fieldName value] := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcore with\n ⟨valueIR, hvalueIR⟩\n exact StmtListGenericCore.cons\n (compiledStmtStep_setStorageAddr_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind)\n (hnoConflict := hnoConflict)\n (hvalueIR := hvalueIR))\n StmtListGenericCore.nil\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Compiler.Constants.evmModulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeAddressSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot\n (value &&& Compiler.Constants.addressMask) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' haddr hnotDyn]\n simp [SourceSemantics.writeAddressSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS,\n Verity.wordToAddress, Verity.Core.Address.ofNat, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Address.modulus, Compiler.Constants.addressMask]\n rw [Nat.mod_eq_of_lt hvalue]\n refine congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat ?_\n simpa [Compiler.Constants.addressMask, Verity.Core.Address.modulus] using\n (Nat.and_two_pow_sub_one_eq_mod (n := 160) value)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n symm\n refine congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat ?_\n have hneqNat := IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq\n have hneqNat' : query.toNat ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneqNat\n apply SourceSemantics.encodeStorageAt_congr\n · simp [SourceSemantics.writeAddressSlots]\n · simp [SourceSemantics.writeAddressSlots, SourceSemantics.wordNormalize, hneqNat']\n · simp [SourceSemantics.writeAddressSlots]\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem compiledStmtStep_setStorageAddr_singleSlot_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ runtime state extraFuel,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] -\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime (.setStorageAddr fieldName value) = sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] =\n irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setStorageAddr fieldName value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR :=\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])]\n have hresolvedSlot : findResolvedFieldAtSlotCopy fields slot =\n some { name := fieldName, ty := FieldType.address } :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots (by rfl)\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n have hMaskedEvalRaw :\n evalIRExpr state\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]) =\n some ((valueNat % Compiler.Constants.evmModulus) &&&\n (Compiler.Constants.addressMask % Compiler.Constants.evmModulus)) := by\n simpa using FunctionBody.evalIRExpr_and_of_eval\n (state := state)\n (lhs := valueIR)\n (rhs := YulExpr.hex Compiler.Constants.addressMask)\n (b := Compiler.Constants.addressMask)\n hIRValue\n (by simp [evalIRExpr, Compiler.Constants.addressMask])\n have hMaskedEval :\n evalIRExpr state\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]) =\n some (valueNat &&& Compiler.Constants.addressMask) := by\n simpa [Nat.mod_eq_of_lt hvalueLt, Compiler.Constants.addressMask] using hMaskedEvalRaw\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot\n (valueNat &&& Compiler.Constants.addressMask) }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorageAddr fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeAddressFieldSlots,\n hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask])\n (valueNat &&& Compiler.Constants.addressMask)\n hMaskedEval\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorageAddr fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n (state := state) (slot := slot)\n (value := valueNat &&& Compiler.Constants.addressMask) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressSlot hruntime hresolvedSlot (by rfl) (by rfl) hvalueLt,\n hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorageAddr_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorageAddr fieldName value)\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] where\n compileOk := by\n have hNotMapping : isMapping fields fieldName = false :=\n isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, hvalueIR]\n preserves := compiledStmtStep_setStorageAddr_singleSlot_preserves\n hcore hinScope hfind hwriteSlots hnoConflict hvalueIR\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nprivate theorem stmtListGenericCore_singleton_setStorageAddr_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {slot : Nat}\n {value : Expr}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorageAddr fieldName value] := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcore with\n ⟨valueIR, hvalueIR⟩\n exact StmtListGenericCore.cons\n (compiledStmtStep_setStorageAddr_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind)\n (hnoConflict := hnoConflict)\n (hvalueIR := hvalueIR))\n StmtListGenericCore.nil\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -381,13 +381,73 @@\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n \n+private theorem list_findSlotPackedNone_ne_none\n+ {seen : List (Nat × String × Option PackedBits)}\n+ {slot : Nat}\n+ (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n+ (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n+ induction seen with\n+ | nil => simp at hmem\n+ | cons entry rest ih =>\n+ simp at hmem\n+ by_cases hEq : entry.1 = slot\n+ · subst hEq\n+ simp only [List.find?]\n+ cases entry.2.2 with\n+ | none => simp [packedSlotsConflict]\n+ | some _ => simp [packedSlotsConflict]\n+ · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n+ rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n+ · exact absurd rfl hEq\n+ · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n+ have hih := ih hrest\n+ change List.find? _ (entry :: rest) ≠ none\n+ rw [List.find?_cons]\n+ split\n+ · simp\n+ · exact hih\n+\n private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n- firstInFieldConflictCopy seen current ≠ none := sorry\n+ firstInFieldConflictCopy seen current ≠ none := by\n+ induction current generalizing seen with\n+ | nil =>\n+ simp at hcurrent\n+ | cons entry rest ih =>\n+ simp at hcurrent\n+ have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n+ have hunpackedRest :\n+ ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n+ intro packed hmem\n+ exact hunpacked packed (by simp [hmem])\n+ -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n+ obtain ⟨e1, e21, e22⟩ := entry\n+ simp at hpnone\n+ subst hpnone\n+ -- Now entry = (e1, e21, none)\n+ rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n+ · -- slot = e1\n+ have hfindSeen := list_findSlotPackedNone_ne_none hseen\n+ simp only [firstInFieldConflictCopy]\n+ cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n+ · exact absurd hf hfindSeen\n+ · simp\n+ · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n+ List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n+ intro hnone\n+ simp only [firstInFieldConflictCopy] at hnone\n+ cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n+ · rw [hfind] at hnone\n+ simp at hnone\n+ have hseen' :\n+ slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n+ simp [hseen]\n+ exact (ih hseen' hrest' hunpackedRest) hnone\n+ · rw [hfind] at hnone; simp at hnone\n \n private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21346,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_75"},"challenge_id":{"kind":"string","value":"e8da6ae65a447190"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":75,"string":"75"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member","depth":1,"n_commands":0,"n_lines":45,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite","n_chars":2292,"n_subproofs":5,"n_tactics":41,"cyclomatic":5,"n_automation":11,"n_rewrites":3,"n_structural":12,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"theorem_name\": \"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 45,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction fields generalizing seen idx with\\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\\n | cons field rest ih =>\\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\\n simp only [firstFieldWriteSlotConflictCopyFrom]\\n by_cases hname : field.name == fieldName\\n · -- field.name matches: hfind and hwrite resolve here\\n simp [hname] at hfind hwrite\\n obtain ⟨rfl, rfl⟩ := hfind\\n subst hwrite\\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\\n -- and all packed bits = field.packedBits = none\\n have htarget_in_entries :\\n SourceSemantics.wordNormalize targetSlot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n simp only [List.mem_cons] at hslot\\n rcases hslot with hslot | halias\\n · subst targetSlot\\n exact fieldWriteEntriesAt_base_mem idx field\\n · exact fieldWriteEntriesAt_alias_mem halias\\n have hunpacked_entries :\\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\\n packed = none := by\\n intro packed hmem\\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\\n hseen htarget_in_entries hunpacked_entries\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | none => exact absurd hc hconflict\\n | some _ => simp\\n · -- field.name doesn't match: recurse\\n simp [hname] at hfind hwrite\\n have hseen' :\\n SourceSemantics.wordNormalize targetSlot ∈\\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\\n (fun entry => entry.1) := by\\n rw [List.map_append, List.mem_append]\\n exact Or.inr hseen\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | some _ => simp\\n | none => exact ih hseen' hfind hwrite\",\n \"n_chars\": 2292,\n \"n_subproofs\": 5,\n \"n_tactics\": 41,\n \"cyclomatic\": 5,\n \"n_automation\": 11,\n \"n_rewrites\": 3,\n \"n_structural\": 12,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked","text":"private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\n","fan_in":1,"n_lines":43,"n_chars":1946,"n_subproofs":6,"n_tactics":34,"cyclomatic":5,"n_automation":13,"n_rewrites":3,"n_structural":10,"automation_only":false,"max_nesting":14}],"string":"[\n {\n \"name\": \"firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\",\n \"text\": \"private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\\n {seen current : List (Nat × String × Option PackedBits)}\\n {slot : Nat}\\n (hseen : slot ∈ seen.map (fun entry => entry.1))\\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\\n firstInFieldConflictCopy seen current ≠ none := by\\n induction current generalizing seen with\\n | nil =>\\n simp at hcurrent\\n | cons entry rest ih =>\\n simp at hcurrent\\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\\n have hunpackedRest :\\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\\n intro packed hmem\\n exact hunpacked packed (by simp [hmem])\\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\\n obtain ⟨e1, e21, e22⟩ := entry\\n simp at hpnone\\n subst hpnone\\n -- Now entry = (e1, e21, none)\\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\\n · -- slot = e1\\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\\n simp only [firstInFieldConflictCopy]\\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\\n · exact absurd hf hfindSeen\\n · simp\\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\\n intro hnone\\n simp only [firstInFieldConflictCopy] at hnone\\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\\n · rw [hfind] at hnone\\n simp at hnone\\n have hseen' :\\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\\n simp [hseen]\\n exact (ih hseen' hrest' hunpackedRest) hnone\\n · rw [hfind] at hnone; simp at hnone\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 43,\n \"n_chars\": 1946,\n \"n_subproofs\": 6,\n \"n_tactics\": 34,\n \"cyclomatic\": 5,\n \"n_automation\": 13,\n \"n_rewrites\": 3,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 14\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListGenericCore_of_supportedStmtList_setStorageSingleSlot_of_surface","fan_in":0,"n_deps_direct":1,"n_deps_transitive":30,"n_lines":21,"n_chars":771,"n_subproofs":0,"n_tactics":7,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"stmtListGenericCore_of_supportedStmtList_setStorageSingleSlot_of_surface\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 30,\n \"n_lines\": 21,\n \"n_chars\": 771,\n \"n_subproofs\": 0,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":24,"string":"24"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := sorry\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\ntheorem stmtListGenericCore_singleton_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {slot : Nat}\n {value : Expr}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorage fieldName value] := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcore with\n ⟨valueIR, hvalueIR⟩\n exact StmtListGenericCore.cons\n (compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind)\n (halias := by rfl)\n (hunpacked := by rfl)\n (hnoConflict := hnoConflict)\n (hnotAddr := by rfl)\n (hnotDyn := by rfl)\n (hnotTransient := by rfl)\n (hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl)\n (hNotAdt := by\n intro name maxFields hty\n cases hty)\n (hvalueIR := hvalueIR))\n StmtListGenericCore.nil\n\ntheorem stmtListGenericCore_of_supportedStmtList_setStorageSingleSlot_of_surface\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorage fieldName value] :=\n stmtListGenericCore_singleton_setStorage_singleSlot\n (fields := fields)\n (scope := scope)\n (hnoConflict := hnoConflict)\n (hfind := hfind)\n (hcore := hcore)\n (hinScope := hinScope)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nprivate theorem encodeStorageAt_writeUintSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot query value : Nat}\n (hneq : query ≠ SourceSemantics.wordNormalize slot) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintSlots world [slot] value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · have hneq' : query ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneq\n simp [SourceSemantics.writeUintSlots, SourceSemantics.wordNormalize, hneq']\n · simp [SourceSemantics.writeUintSlots]\n · simp [SourceSemantics.writeUintSlots]\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeUintSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Verity.Core.Uint256.modulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeUintSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n ·\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' hnotAddr hnotDyn]\n simp [SourceSemantics.writeUintSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS, Verity.Core.Uint256.val_ofNat]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (Nat.mod_eq_of_lt hvalue).symm\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeUintSlots_singleton_other\n (IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\ntheorem compiledStmtStep_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {f : Field}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (halias : f.aliasSlots = [])\n (hunpacked : f.packedBits = none)\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hnotTransient : f.isTransient = false)\n (hNotMapping : isMapping fields fieldName = false)\n (hNotAdt : ∀ name maxFields, f.ty ≠ FieldType.adt name maxFields)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorage fieldName value)\n [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])] where\n compileOk := by\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, halias, hunpacked, hnotTransient, hvalueIR]\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n let compiledIR := [YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])]\n have hresolvedSlot :\n findResolvedFieldAtSlotCopy fields slot = some f :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots hunpacked\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot valueNat }\n set runtime' := { runtime with\n world := SourceSemantics.writeUintSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind, hnotTransient]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorage fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeUintFieldSlots,\n SourceSemantics.writeMappingTargets, hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt (YulExpr.call \"sstore\" [YulExpr.lit slot, valueIR])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot valueIR valueNat hIRValue\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorage fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot (slot := slot) (value := valueNat) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeUintSlot hruntime hresolvedSlot hnotAddr hnotDyn hvalueLt,\n hexact', hbounded, hscope'⟩\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\ntheorem stmtListGenericCore_singleton_setStorage_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {slot : Nat}\n {value : Expr}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorage fieldName value] := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcore with\n ⟨valueIR, hvalueIR⟩\n exact StmtListGenericCore.cons\n (compiledStmtStep_setStorage_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind)\n (halias := by rfl)\n (hunpacked := by rfl)\n (hnoConflict := hnoConflict)\n (hnotAddr := by rfl)\n (hnotDyn := by rfl)\n (hnotTransient := by rfl)\n (hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl)\n (hNotAdt := by\n intro name maxFields hty\n cases hty)\n (hvalueIR := hvalueIR))\n StmtListGenericCore.nil\n\ntheorem stmtListGenericCore_of_supportedStmtList_setStorageSingleSlot_of_surface\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorage fieldName value] :=\n stmtListGenericCore_singleton_setStorage_singleSlot\n (fields := fields)\n (scope := scope)\n (hnoConflict := hnoConflict)\n (hfind := hfind)\n (hcore := hcore)\n (hinScope := hinScope)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -423,6 +423,48 @@\n · simp\n · exact hih\n \n+private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n+ {seen current : List (Nat × String × Option PackedBits)}\n+ {slot : Nat}\n+ (hseen : slot ∈ seen.map (fun entry => entry.1))\n+ (hcurrent : slot ∈ current.map (fun entry => entry.1))\n+ (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n+ firstInFieldConflictCopy seen current ≠ none := by\n+ induction current generalizing seen with\n+ | nil =>\n+ simp at hcurrent\n+ | cons entry rest ih =>\n+ simp at hcurrent\n+ have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n+ have hunpackedRest :\n+ ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n+ intro packed hmem\n+ exact hunpacked packed (by simp [hmem])\n+ -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n+ obtain ⟨e1, e21, e22⟩ := entry\n+ simp at hpnone\n+ subst hpnone\n+ -- Now entry = (e1, e21, none)\n+ rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n+ · -- slot = e1\n+ have hfindSeen := list_findSlotPackedNone_ne_none hseen\n+ simp only [firstInFieldConflictCopy]\n+ cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n+ · exact absurd hf hfindSeen\n+ · simp\n+ · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n+ List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n+ intro hnone\n+ simp only [firstInFieldConflictCopy] at hnone\n+ cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n+ · rw [hfind] at hnone\n+ simp at hnone\n+ have hseen' :\n+ slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n+ simp [hseen]\n+ exact (ih hseen' hrest' hunpackedRest) hnone\n+ · rw [hfind] at hnone; simp at hnone\n+\n private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n@@ -439,7 +481,51 @@\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n- firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := sorry\n+ firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n+ induction fields generalizing seen idx with\n+ | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n+ | cons field rest ih =>\n+ simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n+ simp only [findFieldWriteSlotsCopyFrom] at hwrite\n+ simp only [firstFieldWriteSlotConflictCopyFrom]\n+ by_cases hname : field.name == fieldName\n+ · -- field.name matches: hfind and hwrite resolve here\n+ simp [hname] at hfind hwrite\n+ obtain ⟨rfl, rfl⟩ := hfind\n+ subst hwrite\n+ -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n+ -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n+ -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n+ -- and all packed bits = field.packedBits = none\n+ have htarget_in_entries :\n+ SourceSemantics.wordNormalize targetSlot ∈\n+ (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n+ simp only [List.mem_cons] at hslot\n+ rcases hslot with hslot | halias\n+ · subst targetSlot\n+ exact fieldWriteEntriesAt_base_mem idx field\n+ · exact fieldWriteEntriesAt_alias_mem halias\n+ have hunpacked_entries :\n+ ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n+ packed = none := by\n+ intro packed hmem\n+ exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n+ have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n+ hseen htarget_in_entries hunpacked_entries\n+ cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n+ | none => exact absurd hc hconflict\n+ | some _ => simp\n+ · -- field.name doesn't match: recurse\n+ simp [hname] at hfind hwrite\n+ have hseen' :\n+ SourceSemantics.wordNormalize targetSlot ∈\n+ ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n+ (fun entry => entry.1) := by\n+ rw [List.map_append, List.mem_append]\n+ exact Or.inr hseen\n+ cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n+ | some _ => simp\n+ | none => exact ih hseen' hfind hwrite\n \n theorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21347,"cells":{"task_id":{"kind":"string","value":"ablate_848d26072a8c_76"},"challenge_id":{"kind":"string","value":"da08cf166bb4d54a"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean"},"theory":{"kind":"string","value":"Storage"},"variant":{"kind":"number","value":76,"string":"76"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":97,"string":"97"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member","depth":1,"n_commands":0,"n_lines":45,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite","n_chars":2292,"n_subproofs":5,"n_tactics":41,"cyclomatic":5,"n_automation":11,"n_rewrites":3,"n_structural":12,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"theorem_name\": \"firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 45,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction fields generalizing seen idx with\\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\\n | cons field rest ih =>\\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\\n simp only [firstFieldWriteSlotConflictCopyFrom]\\n by_cases hname : field.name == fieldName\\n · -- field.name matches: hfind and hwrite resolve here\\n simp [hname] at hfind hwrite\\n obtain ⟨rfl, rfl⟩ := hfind\\n subst hwrite\\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\\n -- and all packed bits = field.packedBits = none\\n have htarget_in_entries :\\n SourceSemantics.wordNormalize targetSlot ∈\\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\\n simp only [List.mem_cons] at hslot\\n rcases hslot with hslot | halias\\n · subst targetSlot\\n exact fieldWriteEntriesAt_base_mem idx field\\n · exact fieldWriteEntriesAt_alias_mem halias\\n have hunpacked_entries :\\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\\n packed = none := by\\n intro packed hmem\\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\\n hseen htarget_in_entries hunpacked_entries\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | none => exact absurd hc hconflict\\n | some _ => simp\\n · -- field.name doesn't match: recurse\\n simp [hname] at hfind hwrite\\n have hseen' :\\n SourceSemantics.wordNormalize targetSlot ∈\\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\\n (fun entry => entry.1) := by\\n rw [List.map_append, List.mem_append]\\n exact Or.inr hseen\\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\\n | some _ => simp\\n | none => exact ih hseen' hfind hwrite\",\n \"n_chars\": 2292,\n \"n_subproofs\": 5,\n \"n_tactics\": 41,\n \"cyclomatic\": 5,\n \"n_automation\": 11,\n \"n_rewrites\": 3,\n \"n_structural\": 12,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked","text":"private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\n","fan_in":1,"n_lines":43,"n_chars":1946,"n_subproofs":6,"n_tactics":34,"cyclomatic":5,"n_automation":13,"n_rewrites":3,"n_structural":10,"automation_only":false,"max_nesting":14}],"string":"[\n {\n \"name\": \"firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\",\n \"text\": \"private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\\n {seen current : List (Nat × String × Option PackedBits)}\\n {slot : Nat}\\n (hseen : slot ∈ seen.map (fun entry => entry.1))\\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\\n firstInFieldConflictCopy seen current ≠ none := by\\n induction current generalizing seen with\\n | nil =>\\n simp at hcurrent\\n | cons entry rest ih =>\\n simp at hcurrent\\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\\n have hunpackedRest :\\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\\n intro packed hmem\\n exact hunpacked packed (by simp [hmem])\\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\\n obtain ⟨e1, e21, e22⟩ := entry\\n simp at hpnone\\n subst hpnone\\n -- Now entry = (e1, e21, none)\\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\\n · -- slot = e1\\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\\n simp only [firstInFieldConflictCopy]\\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\\n · exact absurd hf hfindSeen\\n · simp\\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\\n intro hnone\\n simp only [firstInFieldConflictCopy] at hnone\\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\\n · rw [hfind] at hnone\\n simp at hnone\\n have hseen' :\\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\\n simp [hseen]\\n exact (ih hseen' hrest' hunpackedRest) hnone\\n · rw [hfind] at hnone; simp at hnone\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 43,\n \"n_chars\": 1946,\n \"n_subproofs\": 6,\n \"n_tactics\": 34,\n \"cyclomatic\": 5,\n \"n_automation\": 13,\n \"n_rewrites\": 3,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 14\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListGenericCore_of_supportedStmtList_setStorageAddrSingleSlot_of_surface","fan_in":0,"n_deps_direct":1,"n_deps_transitive":30,"n_lines":21,"n_chars":783,"n_subproofs":0,"n_tactics":7,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"stmtListGenericCore_of_supportedStmtList_setStorageAddrSingleSlot_of_surface\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 30,\n \"n_lines\": 21,\n \"n_chars\": 783,\n \"n_subproofs\": 0,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":24,"string":"24"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := sorry\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Compiler.Constants.evmModulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeAddressSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot\n (value &&& Compiler.Constants.addressMask) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' haddr hnotDyn]\n simp [SourceSemantics.writeAddressSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS,\n Verity.wordToAddress, Verity.Core.Address.ofNat, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Address.modulus, Compiler.Constants.addressMask]\n rw [Nat.mod_eq_of_lt hvalue]\n refine congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat ?_\n simpa [Compiler.Constants.addressMask, Verity.Core.Address.modulus] using\n (Nat.and_two_pow_sub_one_eq_mod (n := 160) value)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n symm\n refine congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat ?_\n have hneqNat := IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq\n have hneqNat' : query.toNat ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneqNat\n apply SourceSemantics.encodeStorageAt_congr\n · simp [SourceSemantics.writeAddressSlots]\n · simp [SourceSemantics.writeAddressSlots, SourceSemantics.wordNormalize, hneqNat']\n · simp [SourceSemantics.writeAddressSlots]\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem compiledStmtStep_setStorageAddr_singleSlot_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ runtime state extraFuel,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] -\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime (.setStorageAddr fieldName value) = sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] =\n irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setStorageAddr fieldName value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR :=\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])]\n have hresolvedSlot : findResolvedFieldAtSlotCopy fields slot =\n some { name := fieldName, ty := FieldType.address } :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots (by rfl)\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n have hMaskedEvalRaw :\n evalIRExpr state\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]) =\n some ((valueNat % Compiler.Constants.evmModulus) &&&\n (Compiler.Constants.addressMask % Compiler.Constants.evmModulus)) := by\n simpa using FunctionBody.evalIRExpr_and_of_eval\n (state := state)\n (lhs := valueIR)\n (rhs := YulExpr.hex Compiler.Constants.addressMask)\n (b := Compiler.Constants.addressMask)\n hIRValue\n (by simp [evalIRExpr, Compiler.Constants.addressMask])\n have hMaskedEval :\n evalIRExpr state\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]) =\n some (valueNat &&& Compiler.Constants.addressMask) := by\n simpa [Nat.mod_eq_of_lt hvalueLt, Compiler.Constants.addressMask] using hMaskedEvalRaw\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot\n (valueNat &&& Compiler.Constants.addressMask) }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorageAddr fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeAddressFieldSlots,\n hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask])\n (valueNat &&& Compiler.Constants.addressMask)\n hMaskedEval\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorageAddr fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n (state := state) (slot := slot)\n (value := valueNat &&& Compiler.Constants.addressMask) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressSlot hruntime hresolvedSlot (by rfl) (by rfl) hvalueLt,\n hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorageAddr_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorageAddr fieldName value)\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] where\n compileOk := by\n have hNotMapping : isMapping fields fieldName = false :=\n isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, hvalueIR]\n preserves := compiledStmtStep_setStorageAddr_singleSlot_preserves\n hcore hinScope hfind hwriteSlots hnoConflict hvalueIR\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nprivate theorem stmtListGenericCore_singleton_setStorageAddr_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {slot : Nat}\n {value : Expr}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorageAddr fieldName value] := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcore with\n ⟨valueIR, hvalueIR⟩\n exact StmtListGenericCore.cons\n (compiledStmtStep_setStorageAddr_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind)\n (hnoConflict := hnoConflict)\n (hvalueIR := hvalueIR))\n StmtListGenericCore.nil\n\ntheorem stmtListGenericCore_of_supportedStmtList_setStorageAddrSingleSlot_of_surface\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorageAddr fieldName value] :=\n stmtListGenericCore_singleton_setStorageAddr_singleSlot\n (fields := fields)\n (scope := scope)\n (hnoConflict := hnoConflict)\n (hfind := hfind)\n (hcore := hcore)\n (hinScope := hinScope)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\nattribute [local simp] CompilationModel.compileExprWithInternals_nil_eq\n\nset_option maxHeartbeats 800000 in\nprivate theorem encodeStorageAt_writeUintKeyedMappingSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key query value : Nat}\n (hquery : query < Compiler.Constants.evmModulus)\n (hneq : query ≠ SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key)) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeUintKeyedMappingSlots world [slot] key value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · simp only [SourceSemantics.writeUintKeyedMappingSlots, List.foldl_cons, List.foldl_nil]\n have hneq' :\n query ≠ Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize, Compiler.Proofs.abstractMappingSlot_eq_solidity] using hneq\n have hslotNe :\n IRStorageSlot.ofNat query ≠\n IRStorageSlot.ofNat (Compiler.Proofs.solidityMappingSlot slot key) := by\n intro h\n apply hneq'\n have hnat := congrArg IRStorageSlot.toNat h\n simpa [IRStorageSlot.toNat_ofNat, SourceSemantics.wordNormalize,\n Compiler.Constants.evmModulus, EvmYul.UInt256.size, Nat.mod_eq_of_lt hquery] using hnat\n have hqueryMod : query % Verity.Core.UINT256_MODULUS = query := by\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using\n Nat.mod_eq_of_lt hquery\n simp [Compiler.Proofs.abstractStoreMappingEntry, Compiler.Proofs.abstractMappingSlot,\n hneq', hslotNe, hqueryMod, SourceSemantics.wordNormalize]\n apply Verity.Core.Uint256.ext\n simp [Verity.Core.Uint256.modulus, Nat.mod_eq_of_lt (world.storage query).isLt]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n · simp [SourceSemantics.writeUintKeyedMappingSlots]\n\ndef mappingWordTargetSlot (slot key wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize (Compiler.Proofs.abstractMappingSlot slot key + wordOffset)\n\ndef mapping2WordTargetSlot (slot key1 key2 wordOffset : Nat) : Nat :=\n SourceSemantics.wordNormalize\n (Compiler.Proofs.abstractMappingSlot\n (Compiler.Proofs.abstractMappingSlot slot key1)\n key2 + wordOffset)\n\nprivate theorem IRStorageSlot.toNat_ofNat_wordNormalize (slot : Nat) :\n (IRStorageSlot.ofNat slot).toNat = SourceSemantics.wordNormalize slot := by\n rfl\n\nprivate theorem SourceSemantics.wordNormalize_lt_evmModulus (slot : Nat) :\n SourceSemantics.wordNormalize slot < Compiler.Constants.evmModulus := by\n unfold SourceSemantics.wordNormalize\n exact Nat.mod_lt _ (by norm_num [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS])\n\nprivate theorem IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat\n {query : IRStorageSlot} {slot : Nat}\n (hneq : query ≠ IRStorageSlot.ofNat slot) :\n query.toNat ≠ SourceSemantics.wordNormalize slot := by\n intro h\n apply hneq\n apply IRStorageSlot.eq_of_toNat_eq\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using h\n\nprivate theorem uint256_add_val_eq_mod (a b : Nat) :\n (Verity.Core.Uint256.ofNat a + Verity.Core.Uint256.ofNat b).val =\n (a + b) % Compiler.Constants.evmModulus := by\n change ((a % Compiler.Constants.evmModulus) + (b % Compiler.Constants.evmModulus)) %\n Compiler.Constants.evmModulus =\n (a + b) % Compiler.Constants.evmModulus\n exact (Nat.add_mod a b Compiler.Constants.evmModulus).symm\n\ntheorem mappingWordTargetSlot_eq_uint256_add (slot key wordOffset : Nat) :\n mappingWordTargetSlot slot key wordOffset =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val := by\n unfold mappingWordTargetSlot SourceSemantics.wordNormalize\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset query value : Nat}\n {packed : PackedBits}\n (hneq : query ≠ mappingWordTargetSlot slot key wordOffset) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n query =\n SourceSemantics.encodeStorageAt fields world query := by\n apply SourceSemantics.encodeStorageAt_congr\n · by_cases hEq : query = (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus\n · exfalso\n have htarget : query = mappingWordTargetSlot slot key wordOffset := by\n rw [mappingWordTargetSlot_eq_uint256_add]\n have hslotEq :\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot key)).val =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) % Compiler.Constants.evmModulus := by\n change\n (wordOffset % Compiler.Constants.evmModulus +\n Compiler.Proofs.solidityMappingSlot slot key % Compiler.Constants.evmModulus) %\n Compiler.Constants.evmModulus =\n (Compiler.Proofs.solidityMappingSlot slot key + wordOffset) %\n Compiler.Constants.evmModulus\n rw [Nat.add_comm]\n exact (Nat.add_mod (Compiler.Proofs.solidityMappingSlot slot key) wordOffset\n Compiler.Constants.evmModulus).symm\n exact hEq.trans hslotEq.symm\n exact hneq htarget\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, List.map_cons, List.map_nil]\n intro hbad\n exact False.elim (hEq hbad)\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n · simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n\ndef findResolvedFieldAtSlotCopy (fields : List Field) (slot : Nat) : Option Field :=\n let rec go (remaining : List Field) (idx : Nat) : Option Field :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n go rest (idx + 1)\n go fields 0\n\ndef findResolvedFieldAtSlotCopyFrom\n (fields : List Field) (idx : Nat) (slot : Nat) : Option Field :=\n match fields with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n if SourceSemantics.wordNormalize resolvedSlot = SourceSemantics.wordNormalize slot ||\n (field.aliasSlots.map SourceSemantics.wordNormalize).contains\n (SourceSemantics.wordNormalize slot) then\n some field\n else\n findResolvedFieldAtSlotCopyFrom rest (idx + 1) slot\n\nprivate theorem SourceSemantics.wordNormalize_idem (slot : Nat) :\n SourceSemantics.wordNormalize (SourceSemantics.wordNormalize slot) =\n SourceSemantics.wordNormalize slot := by\n simp [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus]\n\ntheorem findResolvedFieldAtSlotCopy_wordNormalize\n (fields : List Field) (slot : Nat) :\n findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n findResolvedFieldAtSlotCopy fields slot := by\n have hgo :\n ∀ (remaining : List Field) (idx : Nat),\n findResolvedFieldAtSlotCopy.go (SourceSemantics.wordNormalize slot) remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n intro remaining\n induction remaining with\n | nil =>\n intro idx\n rfl\n | cons field rest ih =>\n intro idx\n simp only [findResolvedFieldAtSlotCopy.go]\n rw [SourceSemantics.wordNormalize_idem]\n split\n · rfl\n · exact ih (idx + 1)\n simp only [findResolvedFieldAtSlotCopy]\n exact hgo fields 0\n\ndef findDynamicArrayElementAtSlotCopy\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) : Option Nat :=\n let rec scanElements (baseSlot : Nat) : List Verity.Core.Uint256 → Nat → Option Nat\n | [], _ => none\n | value :: rest, idx =>\n if Compiler.Proofs.solidityMappingSlot baseSlot idx = SourceSemantics.wordNormalize targetSlot then\n some value.val\n else\n scanElements baseSlot rest (idx + 1)\n let rec go (remaining : List Field) (idx : Nat) : Option Nat :=\n match remaining with\n | [] => none\n | field :: rest =>\n let resolvedSlot := field.slot.getD idx\n match field.ty with\n | .dynamicArray _ =>\n match scanElements resolvedSlot (world.storageArray resolvedSlot) 0 with\n | some value => some value\n | none => go rest (idx + 1)\n | _ => go rest (idx + 1)\n go fields 0\n\nprivate def encodeStorageAtCopy\n (fields : List Field) (world : Verity.ContractState) (slot : Nat) : Nat :=\n match findResolvedFieldAtSlotCopy fields slot with\n | some field =>\n if SourceSemantics.fieldUsesAddressStorage field then\n (world.storageAddr slot).val\n else if SourceSemantics.fieldUsesDynamicArrayStorage field then\n (world.storageArray slot).length\n else\n (world.storage slot).val\n | none =>\n match findDynamicArrayElementAtSlotCopy fields world slot with\n | some value => value\n | none => (world.storage slot).val\n\nprivate theorem findResolvedFieldAtSlot_go_eq_copy\n (remaining : List Field) (idx : Nat) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot.go slot remaining idx =\n findResolvedFieldAtSlotCopy.go slot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findResolvedFieldAtSlot.go, findResolvedFieldAtSlotCopy.go]\n split <;> simp_all\n\ntheorem findResolvedFieldAtSlotCopy_eq\n (fields : List Field) (slot : Nat) :\n SourceSemantics.findResolvedFieldAtSlot fields slot =\n findResolvedFieldAtSlotCopy fields slot := by\n simp only [SourceSemantics.findResolvedFieldAtSlot, findResolvedFieldAtSlotCopy]\n exact findResolvedFieldAtSlot_go_eq_copy fields 0 slot\n\nprivate theorem findDynamicArrayElementAtSlot_scanElements_eq_copy\n (baseSlot : Nat) (elems : List Verity.Core.Uint256) (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.scanElements targetSlot baseSlot elems idx =\n findDynamicArrayElementAtSlotCopy.scanElements targetSlot baseSlot elems idx := by\n induction elems generalizing idx with\n | nil => rfl\n | cons v rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.scanElements,\n findDynamicArrayElementAtSlotCopy.scanElements]\n split <;> simp_all\n\nprivate theorem findDynamicArrayElementAtSlot_go_eq_copy\n (remaining : List Field) (world : Verity.ContractState)\n (idx : Nat) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot.go world targetSlot remaining idx =\n findDynamicArrayElementAtSlotCopy.go world targetSlot remaining idx := by\n induction remaining generalizing idx with\n | nil => rfl\n | cons field rest ih =>\n simp only [SourceSemantics.findDynamicArrayElementAtSlot.go,\n findDynamicArrayElementAtSlotCopy.go]\n simp only [findDynamicArrayElementAtSlot_scanElements_eq_copy]\n split\n · split <;> simp_all\n · simp_all\n\ntheorem findDynamicArrayElementAtSlotCopy_eq\n (fields : List Field) (world : Verity.ContractState) (targetSlot : Nat) :\n SourceSemantics.findDynamicArrayElementAtSlot fields world targetSlot =\n findDynamicArrayElementAtSlotCopy fields world targetSlot := by\n simp only [SourceSemantics.findDynamicArrayElementAtSlot, findDynamicArrayElementAtSlotCopy]\n exact findDynamicArrayElementAtSlot_go_eq_copy fields world 0 targetSlot\n\nprivate theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.encodeStorageAt, encodeStorageAtCopy,\n findResolvedFieldAtSlotCopy_eq, findDynamicArrayElementAtSlotCopy_eq]\n split <;> simp_all\n split <;> simp_all\n\nprivate def fieldWriteEntriesAt\n (idx : Nat) (field : Field) : List (Nat × String × Option PackedBits) :=\n firstFieldWriteSlotConflict.fieldOccupiedSlots field (field.slot.getD idx)\n\nprivate theorem fieldWriteEntriesAt_base_mem\n (idx : Nat) (field : Field) :\n SourceSemantics.wordNormalize (field.slot.getD idx) ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n cases ty with\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inl ⟨0, by omega, by simp⟩\n | _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n\nprivate theorem exists_mem_zipIdx_of_mem\n {α : Type} {x : α} {xs : List α} {start : Nat}\n (hmem : x ∈ xs) :\n ∃ i, (x, i) ∈ xs.zipIdx start := by\n induction xs generalizing start with\n | nil => simp at hmem\n | cons y ys ih =>\n simp at hmem\n rcases hmem with rfl | hmem\n · exact ⟨start, by simp [List.zipIdx]⟩\n · obtain ⟨i, hi⟩ := ih (start := start + 1) hmem\n exact ⟨i, by simp [List.zipIdx, hi]⟩\n\nprivate theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtain ⟨name, ty, isTransient, slotOpt, packedBits, aliasSlots⟩ := field\n obtain ⟨aliasIdx, halias⟩ : ∃ i, (slot, i) ∈ aliasSlots.zipIdx :=\n exists_mem_zipIdx_of_mem hmem\n cases ty with\n | uint256 =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | address =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | adt _ maxFields =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨s!\"{name}.aliasSlots[{aliasIdx}]\", none, slot, aliasIdx, halias, 0, by omega, by simp⟩\n | dynamicArray _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingTyped _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n | mappingStruct2 _ _ _ =>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots,\n SourceSemantics.wordNormalize]\n exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩\n\nprivate theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2)) :\n packed = none := by\n obtain ⟨name, ty, slotOpt, packedBits, aliasSlots⟩ := field\n simp at hunpacked\n subst hunpacked\n cases ty <;>\n simp [fieldWriteEntriesAt, firstFieldWriteSlotConflict.fieldOccupiedSlots] at hmem <;>\n aesop\n\nprivate def firstInFieldConflictCopy\n (seen : List (Nat × String × Option PackedBits))\n (current : List (Nat × String × Option PackedBits)) :\n Option (Nat × String × String) :=\n match current with\n | [] => none\n | (slot, ownerName, packed) :: tail =>\n match seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | some (_, prevName, _) => some (slot, prevName, ownerName)\n | none => firstInFieldConflictCopy ((slot, ownerName, packed) :: seen) tail\n\nprivate def firstFieldWriteSlotConflictCopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (idx : Nat) (fields : List Field) : Option (Nat × String × String) :=\n match fields with\n | [] => none\n | field :: rest =>\n let writeSlots := fieldWriteEntriesAt idx field\n match firstInFieldConflictCopy seen writeSlots with\n | some conflict => some conflict\n | none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest\n\nprivate theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 none)) ≠ none := by\n induction seen with\n | nil => simp at hmem\n | cons entry rest ih =>\n simp at hmem\n by_cases hEq : entry.1 = slot\n · subst hEq\n simp only [List.find?]\n cases entry.2.2 with\n | none => simp [packedSlotsConflict]\n | some _ => simp [packedSlotsConflict]\n · have hrest : slot ∈ List.map (fun entry => entry.1) rest := by\n rcases hmem with ⟨rfl, _⟩ | ⟨_, _, hmem'⟩\n · exact absurd rfl hEq\n · exact List.mem_map.mpr ⟨(slot, _, _), hmem', rfl⟩\n have hih := ih hrest\n change List.find? _ (entry :: rest) ≠ none\n rw [List.find?_cons]\n split\n · simp\n · exact hih\n\nprivate theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ current.map (fun entry => entry.1))\n (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n firstInFieldConflictCopy seen current ≠ none := by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | cons entry rest ih =>\n simp at hcurrent\n have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n have hunpackedRest :\n ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n intro packed hmem\n exact hunpacked packed (by simp [hmem])\n -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n obtain ⟨e1, e21, e22⟩ := entry\n simp at hpnone\n subst hpnone\n -- Now entry = (e1, e21, none)\n rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n · -- slot = e1\n have hfindSeen := list_findSlotPackedNone_ne_none hseen\n simp only [firstInFieldConflictCopy]\n cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · exact absurd hf hfindSeen\n · simp\n · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n intro hnone\n simp only [firstInFieldConflictCopy] at hnone\n cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n · rw [hfind] at hnone\n simp at hnone\n have hseen' :\n slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n simp [hseen]\n exact (ih hseen' hrest' hunpackedRest) hnone\n · rw [hfind] at hnone; simp at hnone\n\nprivate theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hseen : SourceSemantics.wordNormalize targetSlot ∈ seen.map (fun entry => entry.1))\n (hfind :\n findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite :\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: hfind and hwrite resolve here\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst hwrite\n -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n -- and all packed bits = field.packedBits = none\n have htarget_in_entries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n simp only [List.mem_cons] at hslot\n rcases hslot with hslot | halias\n · subst targetSlot\n exact fieldWriteEntriesAt_base_mem idx field\n · exact fieldWriteEntriesAt_alias_mem halias\n have hunpacked_entries :\n ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n packed = none := by\n intro packed hmem\n exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n hseen htarget_in_entries hunpacked_entries\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | none => exact absurd hc hconflict\n | some _ => simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n have hseen' :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append]\n exact Or.inr hseen\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some _ => simp\n | none => exact ih hseen' hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n {seen : List (Nat × String × Option PackedBits)}\n (hnoConflict : firstFieldWriteSlotConflictCopyFrom seen idx fields = none)\n (hfind : findFieldWithResolvedSlotCopyFrom fields idx fieldName = some (f, slot))\n (hwrite : findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopyFrom fields idx targetSlot = some f := by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n | cons field rest ih =>\n simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n simp only [findFieldWriteSlotsCopyFrom] at hwrite\n simp only [firstFieldWriteSlotConflictCopyFrom] at hnoConflict\n simp only [findResolvedFieldAtSlotCopyFrom]\n by_cases hname : field.name == fieldName\n · -- field.name matches: f = field, writeSlots = slot :: aliasSlots\n simp [hname] at hfind hwrite\n obtain ⟨rfl, rfl⟩ := hfind\n subst writeSlots\n simp only [List.mem_cons] at hslot\n rcases hslot with rfl | hmem\n · simp\n · rw [show\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot) = true by\n rw [List.contains_eq_mem]\n exact decide_eq_true (List.mem_map.mpr ⟨targetSlot, hmem, rfl⟩)]\n simp\n · -- field.name doesn't match: recurse\n simp [hname] at hfind hwrite\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n | some conflict => rw [hc] at hnoConflict; simp at hnoConflict\n | none =>\n rw [hc] at hnoConflict\n -- After simp, condition is Prop-level: = or ∈\n by_cases hcapture :\n SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot ∨\n ∃ a ∈ field.aliasSlots,\n SourceSemantics.wordNormalize a = SourceSemantics.wordNormalize targetSlot\n · exfalso\n have htargetInEntries :\n SourceSemantics.wordNormalize targetSlot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n rcases hcapture with hbase | ⟨a, haMem, haEq⟩\n · have hb := fieldWriteEntriesAt_base_mem idx field\n rw [hbase] at hb\n exact hb\n · have haIn := fieldWriteEntriesAt_alias_mem (idx := idx) (field := field) haMem\n rw [haEq] at haIn\n exact haIn\n have htargetInSeen :\n SourceSemantics.wordNormalize targetSlot ∈\n ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n (fun entry => entry.1) := by\n rw [List.map_append, List.mem_append, List.map_reverse]\n exact Or.inl (List.mem_reverse.mpr htargetInEntries)\n exact (firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n htargetInSeen hfind hwrite hslot hunpacked) hnoConflict\n · push_neg at hcapture\n rw [show\n (decide (SourceSemantics.wordNormalize (field.slot.getD idx) =\n SourceSemantics.wordNormalize targetSlot) ||\n (List.map SourceSemantics.wordNormalize field.aliasSlots).contains\n (SourceSemantics.wordNormalize targetSlot)) = false by\n simp only [Bool.or_eq_false_iff, decide_eq_false_iff_not,\n List.contains_eq_mem, List.mem_map]\n exact ⟨hcapture.1, by\n intro hmem\n rcases hmem with ⟨a, haMem, haEq⟩\n exact hcapture.2 a haMem haEq⟩]\n exact ih hnoConflict hfind hwrite\n\ntheorem findResolvedFieldAtSlotCopy_go_eq_CopyFrom\n (flds : List Field) (i s : Nat) :\n findResolvedFieldAtSlotCopy.go s flds i = findResolvedFieldAtSlotCopyFrom flds i s := by\n induction flds generalizing i with\n | nil => rfl\n | cons _ _ ih =>\n simp only [findResolvedFieldAtSlotCopy.go, findResolvedFieldAtSlotCopyFrom]\n split <;> simp_all\n\nprivate theorem firstInFieldConflict_eq_Copy\n (seen current : List (Nat × String × Option PackedBits)) :\n firstFieldWriteSlotConflict.go.firstInFieldConflict seen current =\n firstInFieldConflictCopy seen current := by\n induction current generalizing seen with\n | nil => rfl\n | cons entry rest ih =>\n obtain ⟨slot, ownerName, packed⟩ := entry\n simp only [firstFieldWriteSlotConflict_firstInFieldConflict_cons,\n firstInFieldConflictCopy]\n cases seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2 packed) with\n | none => exact ih _\n | some _ => rfl\n\nprivate theorem firstFieldWriteSlotConflict_go_eq_CopyFrom\n (seen : List (Nat × String × Option PackedBits))\n (i : Nat) (flds : List Field) :\n firstFieldWriteSlotConflict.go seen i flds =\n firstFieldWriteSlotConflictCopyFrom seen i flds := by\n induction flds generalizing seen i with\n | nil => rfl\n | cons fld rest ih =>\n rw [firstFieldWriteSlotConflict_go_cons]\n dsimp only []\n rw [firstInFieldConflict_eq_Copy]\n change\n (match firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | some conflict => some conflict\n | none =>\n firstFieldWriteSlotConflict.go\n ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1) rest) =\n firstFieldWriteSlotConflictCopyFrom seen i (fld :: rest)\n simp only [firstFieldWriteSlotConflictCopyFrom]\n cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt i fld) with\n | none =>\n simpa [hc] using ih ((fieldWriteEntriesAt i fld).reverse ++ seen) (i + 1)\n | some _ =>\n simp [hc]\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields targetSlot = some f := by\n -- Bridge result\n show findResolvedFieldAtSlotCopy.go targetSlot fields 0 = some f\n rw [findResolvedFieldAtSlotCopy_go_eq_CopyFrom]\n -- Bridge hypotheses\n have hfindCopy : findFieldWithResolvedSlotCopyFrom fields 0 fieldName = some (f, slot) :=\n findFieldWithResolvedSlot_eq_CopyFrom fields fieldName ▸ hfind\n have hwriteCopy : findFieldWriteSlotsCopyFrom fields 0 fieldName = some writeSlots :=\n findFieldWriteSlots_eq_CopyFrom fields fieldName ▸ hwrite\n have hnoConflictCopy : firstFieldWriteSlotConflictCopyFrom [] 0 fields = none :=\n firstFieldWriteSlotConflict_go_eq_CopyFrom [] 0 fields ▸ hnoConflict\n exact findResolvedFieldAtSlotCopyFrom_of_member\n hnoConflictCopy hfindCopy hwriteCopy hslot hunpacked\n\ntheorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName = some (f, slot))\n (hwrite : findFieldWriteSlots fields fieldName = some [slot])\n (hunpacked : f.packedBits = none) :\n findResolvedFieldAtSlotCopy fields slot = some f := by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n hnoConflict hfind hwrite (by simp) hunpacked\n\nprivate theorem encodeStorageAt_eq_storage_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (hnotAddr : SourceSemantics.fieldUsesAddressStorage f = false)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storage slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]\n\nprivate theorem encodeStorageAt_eq_storageAddr_of_resolvedSlot\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat}\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (_hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false) :\n SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]\n\nprivate theorem encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n {packed : PackedBits}\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n SourceSemantics.encodeStorageAt fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) =\n SourceSemantics.packedWordWrite\n (world.storage (mappingWordTargetSlot slot key wordOffset)).val\n value\n packed := by\n rw [encodeStorageAt_eq_copy]\n simp only [encodeStorageAtCopy, hresolved]\n have harray : (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value).storageArray = world.storageArray := by\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots]\n have hdyn' : findDynamicArrayElementAtSlotCopy fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset) = none := by\n have h1 := findDynamicArrayElementAtSlotCopy_eq fields\n (SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n world [slot] key wordOffset packed value)\n (mappingWordTargetSlot slot key wordOffset)\n have h2 := findDynamicArrayElementAtSlotCopy_eq fields world\n (mappingWordTargetSlot slot key wordOffset)\n rw [← h1, SourceSemantics.findDynamicArrayElementAtSlot_congr_storageArray _ _ _ _ harray,\n h2, hdyn]\n rw [hdyn']\n simp [SourceSemantics.writeAddressKeyedMappingPackedWordSlots, mappingWordTargetSlot,\n SourceSemantics.wordNormalize, SourceSemantics.packedWordWrite,\n Verity.Core.Uint256.val_ofNat]\n have hlt :\n (((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).val <\n Compiler.Constants.evmModulus := by\n exact\n ((((Verity.Core.Uint256.ofNat (world.storage (mappingWordTargetSlot slot key wordOffset)).val).and\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and value (packedMaskNat packed)))).isLt)\n simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt\n\nprivate def abstractStoreStorageOrMappingMany\n (storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord)\n (slots : List Nat) (value : Nat) :\n Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord :=\n match slots with\n | [] => storage\n | slot :: rest =>\n abstractStoreStorageOrMappingMany\n (Compiler.Proofs.abstractStoreStorageOrMapping storage slot value)\n rest\n value\n\nprivate theorem runtimeStateMatchesIR_writeAddressSlot\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {slot value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n {f : Field}\n (hresolved : findResolvedFieldAtSlotCopy fields slot = some f)\n (haddr : SourceSemantics.fieldUsesAddressStorage f = true)\n (hnotDyn : SourceSemantics.fieldUsesDynamicArrayStorage f = false)\n (hvalue : value < Compiler.Constants.evmModulus) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with world := SourceSemantics.writeAddressSlots runtime.world [slot] value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot\n (value &&& Compiler.Constants.addressMask) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n by_cases hEq : query = IRStorageSlot.ofNat slot\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat = some f := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) = some f from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' haddr hnotDyn]\n simp [SourceSemantics.writeAddressSlots, IRStorageSlot.toNat_ofNat_wordNormalize,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS,\n Verity.wordToAddress, Verity.Core.Address.ofNat, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Address.modulus, Compiler.Constants.addressMask]\n rw [Nat.mod_eq_of_lt hvalue]\n refine congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat ?_\n simpa [Compiler.Constants.addressMask, Verity.Core.Address.modulus] using\n (Nat.and_two_pow_sub_one_eq_mod (n := 160) value)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]\n rw [hstorage]\n symm\n refine congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat ?_\n have hneqNat := IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq\n have hneqNat' : query.toNat ≠ slot % Compiler.Constants.evmModulus := by\n simpa [SourceSemantics.wordNormalize] using hneqNat\n apply SourceSemantics.encodeStorageAt_congr\n · simp [SourceSemantics.writeAddressSlots]\n · simp [SourceSemantics.writeAddressSlots, SourceSemantics.wordNormalize, hneqNat']\n · simp [SourceSemantics.writeAddressSlots]\n\nprivate theorem runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n {fields : List Field} {runtime : SourceSemantics.RuntimeState} {state : IRState}\n {slot key wordOffset value : Nat} {packed : PackedBits}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)\n (hresolved :\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot key wordOffset) = none)\n (hdyn :\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot key wordOffset) = none) :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordSlots\n runtime.world [slot] key wordOffset packed value }\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping\n state.storage\n (mappingWordTargetSlot slot key wordOffset)\n (SourceSemantics.packedWordWrite\n (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat (mappingWordTargetSlot slot key wordOffset))))\n value\n packed) } := by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n refine ⟨?_, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain, hret, hevents⟩\n funext query\n set tgt := mappingWordTargetSlot slot key wordOffset with htgt\n by_cases hEq : query = IRStorageSlot.ofNat tgt\n · subst hEq\n rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n have henc : SourceSemantics.encodeStorageAt fields runtime.world tgt =\n (runtime.world.storage tgt).val := by\n rw [encodeStorageAt_eq_copy]; simp only [encodeStorageAtCopy, hresolved, hdyn]\n have htgtNorm : SourceSemantics.wordNormalize tgt = tgt := by\n rw [htgt]\n exact SourceSemantics.wordNormalize_idem _\n have htgtSlot : (IRStorageSlot.ofNat tgt).toNat = tgt := by\n rw [IRStorageSlot.toNat_ofNat_wordNormalize, htgtNorm]\n have htgtLt : tgt < Verity.Core.UINT256_MODULUS := by\n have h := SourceSemantics.wordNormalize_lt_evmModulus tgt\n rw [htgtNorm] at h\n simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using h\n have htgtLtLit :\n mappingWordTargetSlot slot key wordOffset <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [htgt, Verity.Core.UINT256_MODULUS] using htgtLt\n have hstorageLtLit :\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).val <\n 115792089237316195423570985008687907853269984665640564039457584007913129639936 := by\n simpa [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (mappingWordTargetSlot slot key wordOffset)).isLt\n have hencNorm : SourceSemantics.encodeStorageAt fields runtime.world\n (IRStorageSlot.ofNat tgt).toNat = (runtime.world.storage tgt).val := by\n simpa [htgtSlot] using henc\n simp only [hstorage, hencNorm]\n simp [IRStorageWord.toNat_ofNat, EvmYul.UInt256.size,\n Verity.Core.UINT256_MODULUS, Nat.mod_eq_of_lt (runtime.world.storage tgt).isLt]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat (by\n simpa [htgt, Nat.mod_eq_of_lt htgtLtLit, Nat.mod_eq_of_lt hstorageLtLit] using\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_eq_written\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (value := value) hresolved hdyn).symm)\n · rw [Compiler.Proofs.abstractStoreStorageOrMapping_eq]\n simp only [hEq, ↓reduceIte]; rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (encodeStorageAt_writeAddressKeyedMappingPackedWordSlots_singleton_other\n (fields := fields) (world := runtime.world) (slot := slot) (key := key)\n (wordOffset := wordOffset) (packed := packed) (query := query.toNat) (value := value)\n (by simpa [htgt, mappingWordTargetSlot] using\n IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm\n\nprivate theorem bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n {scope : List String}\n {bindings : List (String × Nat)}\n {state : IRState}\n {slot value : Nat}\n (hexact : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings state) :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope bindings\n { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot value } := by\n intro name hname\n simpa [IRState.getVar, Compiler.Proofs.abstractStoreStorageOrMapping_eq] using\n hexact name hname\n\nprivate theorem execIRStmts_single_block_of_continue\n (fuel : Nat)\n (state next : IRState)\n (body : List YulStmt)\n (hbody : execIRStmts fuel state body = .continue next) :\n execIRStmts (fuel + 2) state [YulStmt.block body] = .continue next := by\n have hblock :\n execIRStmt (fuel + 1) state (YulStmt.block body) = .continue next := by\n simpa [execIRStmt, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc] using hbody\n simpa [execIRStmts, hblock]\n\nprivate theorem singletonBlock_sizeOf_slack (body : List YulStmt) :\n sizeOf [YulStmt.block body] - [YulStmt.block body].length = sizeOf body + 2 := by\n simp [YulStmt.block.sizeOf_spec]\n omega\n\nprivate theorem findFieldWriteSlots_of_findFieldWithResolvedSlot\n {fields : List Field} {name : String} {f : Field} {slot : Nat}\n (h : findFieldWithResolvedSlot fields name = some (f, slot)) :\n findFieldWriteSlots fields name = some (slot :: f.aliasSlots) := by\n rw [findFieldWriteSlots_eq_CopyFrom, findFieldWithResolvedSlot_eq_CopyFrom] at *\n revert h\n suffices ∀ idx,\n findFieldWithResolvedSlotCopyFrom fields idx name = some (f, slot) →\n findFieldWriteSlotsCopyFrom fields idx name = some (slot :: f.aliasSlots) by\n exact this 0\n intro idx h\n induction fields generalizing idx with\n | nil => simp [findFieldWithResolvedSlotCopyFrom] at h\n | cons hd tl ih =>\n unfold findFieldWithResolvedSlotCopyFrom at h\n unfold findFieldWriteSlotsCopyFrom\n by_cases hname : hd.name == name\n · rw [if_pos hname] at h ⊢\n simp at h\n rcases h with ⟨hf, hslot⟩\n rw [← hf, ← hslot]\n · rw [if_neg hname] at h ⊢\n exact ih (idx + 1) h\n\nprivate def fieldStoreBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tstore\" else \"sstore\"\n\nprivate def fieldLoadBuiltin (fields : List Field) (fieldName : String) : String :=\n if SourceSemantics.fieldIsTransient fields fieldName then \"tload\" else \"sload\"\n\nprivate theorem compiledStmtStep_setStorageAddr_singleSlot_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ runtime state extraFuel,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] -\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime (.setStorageAddr fieldName value) = sourceResult ∧\n execIRStmts\n ([YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])].length +\n extraFuel + 1)\n state\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] =\n irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setStorageAddr fieldName value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let compiledIR :=\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])]\n have hresolvedSlot : findResolvedFieldAtSlotCopy fields slot =\n some { name := fieldName, ty := FieldType.address } :=\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind hwriteSlots (by rfl)\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hvalueSourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n have hvalueLt := FunctionBody.evalExpr_lt_evmModulus_core_of_scope\n hcore hexact hinScope hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScope)\n hruntime\n rw [hValueSrc] at hvalueLt\n simp at hvalueLt\n have hMaskedEvalRaw :\n evalIRExpr state\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]) =\n some ((valueNat % Compiler.Constants.evmModulus) &&&\n (Compiler.Constants.addressMask % Compiler.Constants.evmModulus)) := by\n simpa using FunctionBody.evalIRExpr_and_of_eval\n (state := state)\n (lhs := valueIR)\n (rhs := YulExpr.hex Compiler.Constants.addressMask)\n (b := Compiler.Constants.addressMask)\n hIRValue\n (by simp [evalIRExpr, Compiler.Constants.addressMask])\n have hMaskedEval :\n evalIRExpr state\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]) =\n some (valueNat &&& Compiler.Constants.addressMask) := by\n simpa [Nat.mod_eq_of_lt hvalueLt, Compiler.Constants.addressMask] using hMaskedEvalRaw\n set state' := { state with\n storage :=\n Compiler.Proofs.abstractStoreStorageOrMapping state.storage slot\n (valueNat &&& Compiler.Constants.addressMask) }\n set runtime' := { runtime with\n world := SourceSemantics.writeAddressSlots runtime.world [slot] valueNat }\n have hfieldTransient :\n SourceSemantics.fieldIsTransient fields fieldName = false := by\n simp [SourceSemantics.fieldIsTransient, hfind]\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setStorageAddr fieldName value) = .continue runtime' := by\n simp [SourceSemantics.execStmt, SourceSemantics.writeAddressFieldSlots,\n hwriteSlots, hValueSrc, hfieldTransient, runtime']\n have hExecStmt :\n execIRStmt (extraFuel + 1) state\n (YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])) =\n .continue state' :=\n execIRStmt_sstore_lit_expr_succ_of_eval\n extraFuel state slot\n (YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask])\n (valueNat &&& Compiler.Constants.addressMask)\n hMaskedEval\n have hfuelEq : 1 + extraFuel = extraFuel + 1 := by omega\n have hIRExec : execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR =\n .continue state' := by\n simp [compiledIR, execIRStmts, hfuelEq, hExecStmt]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setStorageAddr fieldName value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hv | hs\n · exact hinScope n (collectExprNames_mem_exprBoundNames_of_core hcore n hv)\n · exact hs\n have hexact' := FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (bindingsExactlyMatchIRVarsOnScope_writeUintSlot\n (state := state) (slot := slot)\n (value := valueNat &&& Compiler.Constants.addressMask) hexact)\n hincl\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n refine ⟨.continue runtime', .continue state', hSrcExec, hIRExec, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨runtimeStateMatchesIR_writeAddressSlot hruntime hresolvedSlot (by rfl) (by rfl) hvalueLt,\n hexact', hbounded, hscope'⟩\n\ntheorem compiledStmtStep_setStorageAddr_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {valueIR : YulExpr}\n {slot : Nat}\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n CompiledStmtStep fields scope (.setStorageAddr fieldName value)\n [YulStmt.exprStmt\n (YulExpr.call \"sstore\"\n [YulExpr.lit slot,\n YulExpr.call \"and\" [valueIR, YulExpr.hex Compiler.Constants.addressMask]])] where\n compileOk := by\n have hNotMapping : isMapping fields fieldName = false :=\n isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileSetStorage,\n hNotMapping, hfind, hwriteSlots, hvalueIR]\n preserves := compiledStmtStep_setStorageAddr_singleSlot_preserves\n hcore hinScope hfind hwriteSlots hnoConflict hvalueIR\n\nprivate theorem evalIRExpr_mappingSlotChain\n {state : IRState}\n {baseSlot : Nat}\n {keyIRs : List YulExpr}\n {keyVals : List Nat}\n (hkeys : List.Forall₂ (fun exprIR value => evalIRExpr state exprIR = some value) keyIRs keyVals) :\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n (YulExpr.lit baseSlot)) =\n some (SourceSemantics.mappingSlotChain baseSlot keyVals) := by\n have hgeneral :\n ∀ {startExpr : YulExpr} {startSlot : Nat},\n evalIRExpr state startExpr = some startSlot →\n evalIRExpr state\n (keyIRs.foldl\n (fun slotExpr keyExpr => YulExpr.call \"mappingSlot\" [slotExpr, keyExpr])\n startExpr) =\n some (List.foldl Compiler.Proofs.abstractMappingSlot startSlot keyVals) := by\n induction hkeys with\n | nil =>\n intro startExpr startSlot hstart\n simpa using hstart\n | @cons exprIR value keyIRs keyVals hexpr hrest ih =>\n intro startExpr startSlot hstart\n have hnext :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [startExpr, exprIR]) =\n some (Compiler.Proofs.abstractMappingSlot startSlot value) := by\n simp [evalIRExpr, evalIRCall, evalIRExprs, hstart, hexpr,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean]\n simpa [List.foldl] using\n ih (startExpr := YulExpr.call \"mappingSlot\" [startExpr, exprIR])\n (startSlot := Compiler.Proofs.abstractMappingSlot startSlot value) hnext\n simpa [SourceSemantics.mappingSlotChain] using\n hgeneral (startExpr := YulExpr.lit baseSlot) (startSlot := baseSlot) (by simp [evalIRExpr])\n\nprivate theorem execIRStmt_sstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"sstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage\n slotVal valueVal } := by\n cases slotExpr with\n | lit n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | hex n => simp [execIRStmt, evalIRExpr, hvalue, hslot]\n | str s => simp [evalIRExpr] at hslot\n | ident name => simp [execIRStmt, hslot, hvalue]\n | call fname args =>\n cases args with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg rest =>\n cases rest with\n | nil => simp [execIRStmt, hslot, hvalue]\n | cons arg2 rest =>\n cases rest with\n | nil =>\n by_cases hfunc : fname = \"mappingSlot\"\n · subst hfunc\n simp only [evalIRExpr, evalIRCall, evalIRExprs,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] at hslot\n cases hb : evalIRExpr state arg with\n | none => simp [hb] at hslot\n | some bv =>\n cases hk : evalIRExpr state arg2 with\n | none => simp [hb, hk] at hslot\n | some kv =>\n simp [hb, hk] at hslot\n simp [execIRStmt, hb, hk, hvalue,\n Compiler.Proofs.abstractStoreMappingEntry_eq,\n Compiler.Proofs.abstractStoreStorageOrMapping_eq,\n Compiler.Proofs.abstractMappingSlot_eq_solidity, ← hslot]\n · simp [execIRStmt, hslot, hvalue, hfunc]\n | cons arg3 rest => simp [execIRStmt, hslot, hvalue]\n\nprivate theorem execIRStmt_tstore_of_eval\n {state : IRState}\n {slotExpr valueExpr : Compiler.Yul.YulExpr}\n {slotVal valueVal : Nat}\n {fuel : Nat}\n (hslot : evalIRExpr state slotExpr = some slotVal)\n (hvalue : evalIRExpr state valueExpr = some valueVal) :\n execIRStmt (Nat.succ fuel) state\n (Compiler.Yul.YulStmt.exprStmt (Compiler.Yul.YulExpr.call \"tstore\"\n [slotExpr, valueExpr])) =\n .continue { state with\n transientStorage := fun slot =>\n if slot = slotVal % Compiler.Constants.evmModulus then valueVal\n else state.transientStorage slot } := by\n simp [execIRStmt, hslot, hvalue]\n\nprivate theorem uint256_and_val_eq_land_mod (a b : Nat) :\n (Verity.Core.Uint256.and a b).val =\n ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.and, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have hlt : Nat.land (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.and_lt_two_pow (a % Compiler.Constants.evmModulus)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_or_val_eq_lor_mod (a b : Nat) :\n (Verity.Core.Uint256.or a b).val =\n ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n simp only [Verity.Core.Uint256.or, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS]\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have hlt : Nat.lor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) <\n Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n exact Nat.or_lt_two_pow\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha)\n (by simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using hb)\n exact Nat.mod_eq_of_lt hlt\n\nprivate theorem uint256_not_val_eq_xor_allOnes_mod (a : Nat) :\n (Verity.Core.Uint256.not a).val =\n Nat.xor (a % Compiler.Constants.evmModulus) (Compiler.Constants.evmModulus - 1) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus := by\n exact Nat.mod_lt _ (by simp [Compiler.Constants.evmModulus])\n have ha256 : a % Compiler.Constants.evmModulus < 2 ^ 256 := by\n simpa [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl] using ha\n have hxor_eq : Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n have key :\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat =\n 2 ^ 256 - 1 - (a % Compiler.Constants.evmModulus) := by\n rw [BitVec.xor_allOnes]\n simp only [BitVec.toNat_not, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256]\n have lhs_eq :\n Nat.xor (a % Compiler.Constants.evmModulus) (2 ^ 256 - 1) =\n (BitVec.ofNat 256 (a % Compiler.Constants.evmModulus) ^^^ BitVec.allOnes 256).toNat := by\n simp only [BitVec.toNat_xor, BitVec.toNat_ofNat, Nat.mod_eq_of_lt ha256, BitVec.toNat_allOnes]\n rfl\n rw [lhs_eq, key]\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n simp only [Verity.Core.Uint256.not, Verity.Core.Uint256.val_ofNat, Verity.Core.MAX_UINT256,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n rw [hxor_eq, Nat.mod_eq_of_lt (by omega : 2 ^ 256 - 1 - (a % 2 ^ 256) < 2 ^ 256)]\n\nprivate theorem uint256_shl_val_eq_mul_pow_mod\n (shift value : Nat)\n (hshift : shift < 256) :\n (Verity.Core.Uint256.shl shift value).val =\n ((value % Compiler.Constants.evmModulus) * 2 ^ shift) % Compiler.Constants.evmModulus := by\n have hshiftLt : shift < Compiler.Constants.evmModulus := by\n rw [show Compiler.Constants.evmModulus = 2 ^ 256 by rfl]\n omega\n simp only [Verity.Core.Uint256.shl, Verity.Core.Uint256.val_ofNat,\n Verity.Core.Uint256.modulus, Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS,\n Nat.mod_eq_of_lt hshiftLt]\n rw [Nat.shiftLeft_eq]\n\nset_option maxHeartbeats 0 in\nset_option maxRecDepth 10000 in\nprivate theorem compiledStmtStep_setMappingPackedWord_singleSlot_of_slotSafety_preserves\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {key value : Expr}\n {wordOffset : Nat}\n {packed : PackedBits}\n {keyIR valueIR : YulExpr}\n {slot : Nat}\n (hcoreKey : FunctionBody.ExprCompileCore key)\n (hinScopeKey : FunctionBody.exprBoundNamesInScope key scope)\n (hcoreValue : FunctionBody.ExprCompileCore value)\n (hinScopeValue : FunctionBody.exprBoundNamesInScope value scope)\n (hcompatValue : \"__compat_value\" ∉ scope)\n (hcompatPacked : \"__compat_packed\" ∉ scope)\n (hcompatSlotWord : \"__compat_slot_word\" ∉ scope)\n (hcompatSlotCleared : \"__compat_slot_cleared\" ∉ scope)\n (hpacked : packedBitsValid packed = true)\n (hwriteSlots : findFieldWriteSlots fields fieldName = some [slot])\n (hslotSafety :\n ∀ runtime keyNat,\n SourceSemantics.evalExpr fields runtime key = some keyNat →\n findResolvedFieldAtSlotCopy fields\n (mappingWordTargetSlot slot keyNat wordOffset) = none ∧\n findDynamicArrayElementAtSlotCopy fields runtime.world\n (mappingWordTargetSlot slot keyNat wordOffset) = none)\n (hkeyIR : CompilationModel.compileExpr fields .calldata key = Except.ok keyIR)\n (hvalueIR : CompilationModel.compileExpr fields .calldata value = Except.ok valueIR) :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (extraFuel : Nat),\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n sizeOf [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] -\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length ≤\n extraFuel →\n ∃ sourceResult irExec,\n SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) = sourceResult ∧\n execIRStmts\n ([YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]].length +\n extraFuel + 1)\n state\n [YulStmt.block\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\",\n YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\"\n (YulExpr.call (fieldLoadBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase\n else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset],\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])]] = irExec ∧\n stmtStepMatchesIRExec fields\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n sourceResult\n irExec := by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n let writeSlotExpr :=\n let mappingBase := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]\n if wordOffset == 0 then mappingBase else YulExpr.call \"add\" [mappingBase, YulExpr.lit wordOffset]\n let blockBody :=\n [ YulStmt.let_ \"__compat_value\" valueIR\n , YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])\n , YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])\n , YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])\n , YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\"\n [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]]) ]\n let compiledIR := [YulStmt.block blockBody]\n have hkeySourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntime\n have hvalueSourceEval :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreValue hexact hinScopeValue hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeValue)\n hruntime\n rw [hkeyIR] at hkeySourceEval\n rw [hvalueIR] at hvalueSourceEval\n simp [Except.toOption] at hkeySourceEval hvalueSourceEval\n rcases hIRKey : evalIRExpr state keyIR with _ | keyNat\n · simp [hIRKey, Option.bind] at hkeySourceEval\n · simp [hIRKey, Option.bind] at hkeySourceEval\n rcases hIRValue : evalIRExpr state valueIR with _ | valueNat\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n · simp [hIRValue, Option.bind] at hvalueSourceEval\n have hKeySrc : SourceSemantics.evalExpr fields runtime key = some keyNat :=\n hkeySourceEval.symm\n have hValueSrc : SourceSemantics.evalExpr fields runtime value = some valueNat :=\n hvalueSourceEval.symm\n rcases hslotSafety runtime keyNat hKeySrc with ⟨hresolvedNone, hdynNone⟩\n set targetSlot := mappingWordTargetSlot slot keyNat wordOffset\n set oldWordNat :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n state.transientStorage (SourceSemantics.wordNormalize targetSlot)\n else\n Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat targetSlot))\n set storedWordNat := SourceSemantics.packedWordWrite oldWordNat valueNat packed\n have hMappingBaseEval :\n evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKey] : List.Forall₂\n (fun exprIR value => evalIRExpr state exprIR = some value)\n [keyIR] [keyNat]))\n have hpackedOffsetLt : packed.offset < 256 := by\n have hvalid := hpacked\n simp [CompilationModel.packedBitsValid] at hvalid\n omega\n have hWriteSlotEval : evalIRExpr state writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n set state1 := state.setVar \"__compat_value\" valueNat\n have hCompatValue :\n ∀ fuel, execIRStmt (fuel + 1) state (YulStmt.let_ \"__compat_value\" valueIR) =\n .continue state1 := by\n intro fuel\n simp [state1, execIRStmt, hIRValue]\n have hPackedEval :\n evalIRExpr state1\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)]) =\n some (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val := by\n simpa [uint256_and_val_eq_land_mod] using\n FunctionBody.evalIRExpr_and_of_eval\n (state := state1)\n (lhs := YulExpr.ident \"__compat_value\")\n (rhs := YulExpr.lit (packedMaskNat packed))\n (a := valueNat)\n (b := packedMaskNat packed)\n (by simp [evalIRExpr, state1, IRState.getVar, IRState.setVar])\n (by simp [evalIRExpr])\n set state2 := state1.setVar \"__compat_packed\" (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val\n have hCompatPacked :\n ∀ fuel, execIRStmt (fuel + 1) state1\n (YulStmt.let_ \"__compat_packed\"\n (YulExpr.call \"and\" [YulExpr.ident \"__compat_value\", YulExpr.lit (packedMaskNat packed)])) =\n .continue state2 := by\n intro fuel\n simp [state2, execIRStmt, hPackedEval]\n have hexact_state1 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := valueNat) hexact hcompatValue\n have hexact_state2 :\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact_state1 hcompatPacked\n have hruntimeCompat1 : FunctionBody.runtimeStateMatchesIR fields runtime state1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntimeCompat2 : FunctionBody.runtimeStateMatchesIR fields runtime state2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntimeCompat1\n have hIRKeyState2 : evalIRExpr state2 keyIR = some keyNat := by\n have h := FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state2 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat2\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state2 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval2 :\n evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state2)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState2] : List.Forall₂\n (fun exprIR value => evalIRExpr state2 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval2 : evalIRExpr state2 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state2 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval2)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state2)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval2\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state2\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSlotWordEval :\n evalIRExpr state2 (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr]) = some oldWordNat := by\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htrans, oldWordNat, state2, state1,\n SourceSemantics.wordNormalize,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (state.transientStorage (a % Compiler.Constants.evmModulus))))\n hWriteSlotEval2\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [evalIRExpr, evalIRCall, evalIRExprs,\n fieldLoadBuiltin, htransFalse, oldWordNat, state2, state1,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallWithEvmYulLeanContext,\n Compiler.Proofs.YulGeneration.Backends.evalBuiltinCallViaEvmYulLean] using\n congrArg\n (fun r => r.bind (fun a =>\n some (Compiler.Proofs.IRGeneration.IRStorageWord.toNat\n (state.storage (IRStorageSlot.ofNat a)))))\n hWriteSlotEval2\n set state3 := state2.setVar \"__compat_slot_word\" oldWordNat\n have hexact_state3 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state2 hcompatSlotWord\n have hruntimeCompat3 : FunctionBody.runtimeStateMatchesIR fields runtime state3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat2\n have hCompatSlotWord :\n ∀ fuel, execIRStmt (fuel + 1) state2\n (YulStmt.let_ \"__compat_slot_word\" (YulExpr.call (fieldLoadBuiltin fields fieldName) [writeSlotExpr])) =\n .continue state3 := by\n intro fuel\n simp [state3, execIRStmt, hSlotWordEval]\n have hSlotClearedEval :\n evalIRExpr state3\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]]) =\n some (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotEval :\n evalIRExpr state3\n (YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]) =\n some (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val := by\n simpa [uint256_not_val_eq_xor_allOnes_mod] using\n (FunctionBody.evalIRExpr_not_of_eval\n (state := state3)\n (expr := YulExpr.lit (packedShiftedMaskNat packed))\n (value := packedShiftedMaskNat packed)\n (by simp [evalIRExpr]))\n have hAndEval :=\n FunctionBody.evalIRExpr_and_of_eval\n (state := state3)\n (lhs := YulExpr.ident \"__compat_slot_word\")\n (rhs := YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)])\n (a := oldWordNat)\n (b := (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val)\n (by simp [evalIRExpr, state3, state2, state1, IRState.getVar, IRState.setVar])\n hNotEval\n have hAndBridge :\n ((oldWordNat % Compiler.Constants.evmModulus) &&&\n ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val %\n Compiler.Constants.evmModulus)) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val := by\n have hNotLt :\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed)).isLt\n have hNotOfNat :\n Verity.Core.Uint256.ofNat ((Verity.Core.Uint256.not (packedShiftedMaskNat packed)).val) =\n Verity.Core.Uint256.not (packedShiftedMaskNat packed) := by\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hNotLt]\n simpa [Nat.mod_eq_of_lt hNotLt, hNotOfNat] using\n (uint256_and_val_eq_land_mod oldWordNat\n ((Verity.Core.Uint256.ofNat (packedShiftedMaskNat packed)).not.val)).symm\n simpa [hAndBridge] using hAndEval\n set state4 := state3.setVar \"__compat_slot_cleared\"\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val\n have hexact_state4 : FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant hexact_state3 hcompatSlotCleared\n have hruntimeCompat4 : FunctionBody.runtimeStateMatchesIR fields runtime state4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant hruntimeCompat3\n have hCompatSlotCleared :\n ∀ fuel, execIRStmt (fuel + 1) state3\n (YulStmt.let_ \"__compat_slot_cleared\"\n (YulExpr.call \"and\"\n [YulExpr.ident \"__compat_slot_word\",\n YulExpr.call \"not\" [YulExpr.lit (packedShiftedMaskNat packed)]])) =\n .continue state4 := by\n intro fuel\n simp [state4, execIRStmt, hSlotClearedEval]\n have hStoredEval :\n evalIRExpr state4\n (YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]) =\n some storedWordNat := by\n have hpackedOffsetLtMod : packed.offset < Compiler.Constants.evmModulus := by\n have hevmmodGt256 : 256 < Compiler.Constants.evmModulus := by\n decide\n exact lt_trans hpackedOffsetLt hevmmodGt256\n have hShlEval :\n evalIRExpr state4\n (YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]) =\n some (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val := by\n simpa [Nat.mod_eq_of_lt hpackedOffsetLtMod, uint256_shl_val_eq_mul_pow_mod, hpackedOffsetLt] using\n (FunctionBody.evalIRExpr_shl_of_eval\n (state := state4)\n (shiftExpr := YulExpr.lit packed.offset)\n (valueExpr := YulExpr.ident \"__compat_packed\")\n (shift := packed.offset)\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n (by simp [evalIRExpr])\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar]))\n have hOrEval :=\n FunctionBody.evalIRExpr_or_of_eval\n (state := state4)\n (lhs := YulExpr.ident \"__compat_slot_cleared\")\n (rhs := YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"])\n (a := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n (b := (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)\n (by simp [evalIRExpr, state4, state3, state2, state1, IRState.getVar, IRState.setVar])\n hShlEval\n have hClearedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val) =\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))) := by\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hClearedLt]\n have hShiftedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val) =\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) := by\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hShiftedLt]\n have hPackedOfNat :\n Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val) =\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)) := by\n have hPackedLt :\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).isLt\n ext\n simp [Verity.Core.Uint256.val_ofNat, Nat.mod_eq_of_lt hPackedLt]\n have hClearedLt :\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).isLt\n have hShiftedLt :\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val <\n Compiler.Constants.evmModulus :=\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).isLt\n have hOrBridge :\n ((((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val %\n Compiler.Constants.evmModulus) |||\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val %\n Compiler.Constants.evmModulus))) =\n (((Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)).or\n (Verity.Core.Uint256.ofNat\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val))).val) := by\n simpa [uint256_or_val_eq_lor_mod, Nat.mod_eq_of_lt hClearedLt, Nat.mod_eq_of_lt hShiftedLt]\n using\n (uint256_or_val_eq_lor_mod\n ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n ((Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val).val)).symm\n rw [hOrBridge] at hOrEval\n rw [hShiftedOfNat] at hOrEval\n simpa [storedWordNat, SourceSemantics.packedWordWrite, hClearedOfNat, hPackedOfNat]\n using hOrEval\n set state' :=\n if SourceSemantics.fieldIsTransient fields fieldName then\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then\n storedWordNat\n else\n state4.transientStorage o }\n else\n { state4 with\n storage := Compiler.Proofs.abstractStoreStorageOrMapping state.storage targetSlot storedWordNat }\n have hIRKeyState4 : evalIRExpr state4 keyIR = some keyNat := by\n have h :=\n FunctionBody.eval_compileExpr_core_of_scope\n hcoreKey hexact_state4 hinScopeKey hbounded\n (FunctionBody.exprBoundNamesPresent_of_scope hscope hinScopeKey)\n hruntimeCompat4\n rw [hkeyIR] at h\n simp [Except.toOption, hKeySrc] at h\n cases h' : evalIRExpr state4 keyIR <;> simp [h'] at h\n simpa using congrArg some h\n have hMappingBaseEval4 :\n evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.abstractMappingSlot slot keyNat) := by\n simpa using\n (evalIRExpr_mappingSlotChain\n (state := state4)\n (baseSlot := slot)\n (keyIRs := [keyIR])\n (keyVals := [keyNat])\n (by simp [hIRKeyState4] : List.Forall₂\n (fun exprIR value => evalIRExpr state4 exprIR = some value)\n [keyIR] [keyNat]))\n have hWriteSlotEval4 : evalIRExpr state4 writeSlotExpr = some targetSlot := by\n dsimp [writeSlotExpr, targetSlot]\n by_cases hzero : wordOffset = 0\n · subst hzero\n have hlt :\n Compiler.Proofs.solidityMappingSlot slot keyNat < Compiler.Constants.evmModulus := by\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (Compiler.Proofs.abstractMappingSlot_lt_evmModulus slot keyNat)\n simpa [Verity.Core.Uint256.val_ofNat, mappingWordTargetSlot, SourceSemantics.wordNormalize,\n Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n (show evalIRExpr state4 (YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR]) =\n some (Compiler.Proofs.solidityMappingSlot slot keyNat % Compiler.Constants.evmModulus) by\n simpa [Nat.mod_eq_of_lt hlt, Compiler.Proofs.abstractMappingSlot_eq_solidity] using\n hMappingBaseEval4)\n · have hAddEval :=\n FunctionBody.evalIRExpr_add_of_eval\n (state := state4)\n (lhs := YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR])\n (rhs := YulExpr.lit wordOffset)\n (a := Compiler.Proofs.abstractMappingSlot slot keyNat)\n (b := wordOffset)\n hMappingBaseEval4\n (by simp [evalIRExpr])\n have hAddEval' :\n evalIRExpr state4\n (YulExpr.call \"add\"\n [YulExpr.call \"mappingSlot\" [YulExpr.lit slot, keyIR], YulExpr.lit wordOffset]) =\n some ((Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat (Compiler.Proofs.solidityMappingSlot slot keyNat)).val) := by\n rw [uint256_add_val_eq_mod]\n simpa [Compiler.Proofs.abstractMappingSlot_eq_solidity, Nat.add_assoc, Nat.add_comm,\n Nat.add_left_comm] using hAddEval\n simpa [hzero, targetSlot, mappingWordTargetSlot_eq_uint256_add] using hAddEval'\n have hSstore :\n ∀ fuel, execIRStmt (fuel + 1) state4\n (YulStmt.exprStmt\n (YulExpr.call (fieldStoreBuiltin fields fieldName)\n [writeSlotExpr,\n YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]]])) =\n .continue state' := by\n intro fuel\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [fieldStoreBuiltin, htrans, state', state4, state3, state2, state1,\n SourceSemantics.wordNormalize] using\n (execIRStmt_tstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [fieldStoreBuiltin, htransFalse, state', state4, state3, state2, state1] using\n (execIRStmt_sstore_of_eval\n (state := state4)\n (slotExpr := writeSlotExpr)\n (valueExpr := YulExpr.call \"or\"\n [YulExpr.ident \"__compat_slot_cleared\",\n YulExpr.call \"shl\" [YulExpr.lit packed.offset, YulExpr.ident \"__compat_packed\"]])\n (slotVal := targetSlot)\n (valueVal := storedWordNat)\n (fuel := fuel)\n hWriteSlotEval4\n hStoredEval)\n have hSizeOfListBound : ∀ (l : List YulStmt), l.length + 1 ≤ sizeOf l := by\n intro l\n induction l with\n | nil => simp\n | cons h t ih =>\n show t.length + 1 + 1 ≤ 1 + sizeOf h + sizeOf t\n omega\n have hbodyFuelLe : 6 ≤ extraFuel := by\n have hBodyLen : blockBody.length = 5 := by\n simp [blockBody]\n have hBodyBound := hSizeOfListBound blockBody\n have hBlockSizeOf : 6 ≤ sizeOf [YulStmt.block blockBody] - [YulStmt.block blockBody].length := by\n rw [singletonBlock_sizeOf_slack]\n omega\n exact le_trans hBlockSizeOf hslack\n let bodyExtraFuel := extraFuel - 6\n have hbodyFuelEq : bodyExtraFuel + 6 = extraFuel := by\n dsimp [bodyExtraFuel]\n omega\n have hBody :\n execIRStmts extraFuel state blockBody = .continue state' := by\n rw [← hbodyFuelEq]\n simp [execIRStmts, blockBody, bodyExtraFuel,\n hCompatValue (bodyExtraFuel + 4),\n hCompatPacked (bodyExtraFuel + 3),\n hCompatSlotWord (bodyExtraFuel + 2),\n hCompatSlotCleared (bodyExtraFuel + 1),\n hSstore bodyExtraFuel]\n have hWhole :\n execIRStmts (compiledIR.length + extraFuel + 1) state compiledIR = .continue state' := by\n have hblock := execIRStmts_single_block_of_continue\n extraFuel state state' blockBody hBody\n simpa [compiledIR, Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hblock\n have hSrcExec : SourceSemantics.execStmt fields runtime\n (.setMappingPackedWord fieldName key wordOffset packed value) =\n .continue\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat } := by\n simp [SourceSemantics.execStmt, hwriteSlots, hKeySrc, hValueSrc, hpacked,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots]\n have hincl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value)) scope := by\n intro n hn\n simp [stmtNextScope, collectStmtNames] at hn\n rcases hn with hk | hv | hs\n · exact hinScopeKey n (collectExprNames_mem_exprBoundNames_of_core hcoreKey n hk)\n · exact hinScopeValue n (collectExprNames_mem_exprBoundNames_of_core hcoreValue n hv)\n · exact hs\n have hscope' := FunctionBody.scopeNamesPresent_of_included hscope hincl\n have hruntime1 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_value\") (value := valueNat) hruntime\n have hruntime2 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hruntime1\n have hruntime3 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_word\") (value := oldWordNat) hruntime2\n have hruntime4 :=\n FunctionBody.runtimeStateMatchesIR_setVar_irrelevant\n (name := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hruntime3\n have hruntime' :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n state' := by\n have hstoredLt : storedWordNat < Compiler.Constants.evmModulus := by\n dsimp [storedWordNat, SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · have hmatch :\n FunctionBody.runtimeStateMatchesIR fields\n { runtime with\n world := SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots\n fields fieldName runtime.world [slot] keyNat wordOffset packed valueNat }\n { state4 with\n transientStorage := fun o =>\n if o = SourceSemantics.wordNormalize targetSlot then storedWordNat\n else state4.transientStorage o } := by\n rcases hruntime4 with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchain,\n hret, hevents⟩\n refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩\n · funext query\n rw [hstorage]\n exact congrArg Compiler.Proofs.IRGeneration.IRStorageWord.ofNat\n (SourceSemantics.encodeStorageAt_congr\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans])\n (by simp [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans]))\n · funext query\n have htargetNorm : SourceSemantics.wordNormalize targetSlot = targetSlot := by\n simpa [targetSlot, mappingWordTargetSlot] using\n SourceSemantics.wordNormalize_idem\n (Compiler.Proofs.abstractMappingSlot slot keyNat + wordOffset)\n by_cases hquery : query = targetSlot\n · subst hquery\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hTargetMod, htransient, Nat.mod_eq_of_lt hstoredLt]\n have hstateTransient :\n state.transientStorage targetSlot =\n (runtime.world.transientStorage targetSlot).val := by\n have hstate4Transient :\n state4.transientStorage targetSlot =\n state.transientStorage targetSlot := by\n simp [state4, state3, state2, state1, IRState.setVar]\n rw [← hstate4Transient]\n exact congrFun htransient targetSlot\n rw [hstateTransient]\n exact (Nat.mod_eq_of_lt (by\n dsimp [SourceSemantics.packedWordWrite]\n exact ((Verity.Core.Uint256.and (runtime.world.transientStorage targetSlot).val\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).or\n (Verity.Core.Uint256.shl packed.offset\n (Verity.Core.Uint256.and valueNat (packedMaskNat packed)))).isLt)).symm\n · have hbeq : (targetSlot == query) = false := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simp [BEq.beq, hqueryRev]\n have hTargetMod :\n (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = targetSlot := by\n rw [show targetSlot =\n (Verity.Core.Uint256.ofNat wordOffset +\n Verity.Core.Uint256.ofNat\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).val by\n simpa [targetSlot] using mappingWordTargetSlot_eq_uint256_add slot keyNat wordOffset]\n simpa [Nat.add_comm] using\n (uint256_add_val_eq_mod wordOffset\n (Compiler.Proofs.solidityMappingSlot slot keyNat)).symm\n have htargetModSelf : targetSlot % Compiler.Constants.evmModulus = targetSlot := by\n exact Nat.mod_eq_of_lt (SourceSemantics.wordNormalize_lt_evmModulus _)\n have hqueryTarget :\n ¬ (Compiler.Proofs.solidityMappingSlot slot keyNat + wordOffset) %\n Compiler.Constants.evmModulus = query := by\n have hqueryRev : ¬ targetSlot = query := by\n intro h\n exact hquery h.symm\n simpa [hTargetMod] using hqueryRev\n simp [oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans,\n htargetNorm, htargetModSelf, hquery, hbeq, hqueryTarget, htransient]\n exact congrFun htransient query\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hsender\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hmsgValue\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hthis\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using htimestamp\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hblock\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hchain\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hret\n · simpa [SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htrans] using hevents\n simpa [state', htrans] using hmatch\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [state', targetSlot, oldWordNat, storedWordNat,\n SourceSemantics.writeAddressKeyedMappingPackedWordFieldSlots, htransFalse] using\n runtimeStateMatchesIR_writeAddressKeyedMappingPackedWordSlot\n (runtime := runtime)\n (state := state4)\n (slot := slot) (key := keyNat) (wordOffset := wordOffset) (packed := packed)\n (value := valueNat) hruntime4 hresolvedNone hdynNone\n have hexact1 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_value\") (value := valueNat) hexact hcompatValue\n have hexact2 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_packed\")\n (value := (Verity.Core.Uint256.and valueNat (packedMaskNat packed)).val)\n hexact1 hcompatPacked\n have hexact3 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_word\") (value := oldWordNat)\n hexact2 hcompatSlotWord\n have hexact4 :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_irrelevant\n (tempName := \"__compat_slot_cleared\")\n (value := (Verity.Core.Uint256.and oldWordNat\n (Verity.Core.Uint256.not (packedShiftedMaskNat packed))).val)\n hexact3 hcompatSlotCleared\n have hexact' : FunctionBody.bindingsExactlyMatchIRVarsOnScope\n (stmtNextScope scope (.setMappingPackedWord fieldName key wordOffset packed value))\n runtime.bindings state' :=\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (by\n intro name hname\n by_cases htrans : SourceSemantics.fieldIsTransient fields fieldName = true\n · simpa [IRState.getVar, state', htrans] using hexact4 name hname\n · have htransFalse : SourceSemantics.fieldIsTransient fields fieldName = false := by\n cases h : SourceSemantics.fieldIsTransient fields fieldName <;> simp [h] at htrans ⊢\n simpa [IRState.getVar, state', htransFalse] using hexact4 name hname)\n hincl\n refine ⟨_, _, hSrcExec, hWhole, ?_⟩\n simp [stmtStepMatchesIRExec]\n exact ⟨hruntime', hexact', hbounded, hscope'⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageField\n {fields : List Field}\n {scope : List String}\n {tmp fieldName : String}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.uint256 }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storage fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_uint256 hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storage fieldName) =\n some (runtime.world.storage (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) => some (SourceSemantics.readFieldWord runtime.world field s).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.uint256 } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.uint256 } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storage_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storage (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storage fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storage fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS] using\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v\n (runtime.world.storage (SourceSemantics.wordNormalize slot)).isLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_letStorageAddrField\n {fields : List Field} {scope : List String} {tmp fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.letVar tmp (Expr.storageAddr fieldName))\n [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar tmp v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings tmp v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.letVar tmp (Expr.storageAddr fieldName))) (tmp :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings tmp r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.let_ tmp (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar tmp)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime tmp v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded tmp v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nset_option maxHeartbeats 800000 in\nprivate theorem compiledStmtStep_assignStorageAddrField\n {fields : List Field} {scope : List String} {name fieldName : String} {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hfieldInScope : fieldName ∈ scope) :\n CompiledStmtStep fields scope (.assignVar name (Expr.storageAddr fieldName))\n [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])] where\n compileOk := by\n have hNotMapping := isMapping_false_of_findFieldWithResolvedSlot_address hfind rfl\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork, CompilationModel.compileExprWithInternals,\n hNotMapping, hfind]\n rfl\n preserves runtime state extraFuel hexact hscope hbounded hruntime hslack := by\n have hEvalSrc : SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) =\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val := by\n change (match findFieldWithResolvedSlot fields fieldName with\n | some (field, s) =>\n if field.isTransient then\n some (runtime.world.transientStorage (SourceSemantics.wordNormalize s)).val\n else\n some (runtime.world.storageAddr (SourceSemantics.wordNormalize s)).val\n | none => none) = _\n rw [hfind]\n rfl\n have hresolved := findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton\n hnoConflict hfind\n (by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind) (by rfl)\n have hIR := FunctionBody.evalIRExpr_sload_of_runtimeStateMatchesIR hruntime slot\n have hresolved' :\n findResolvedFieldAtSlotCopy fields (IRStorageSlot.ofNat slot).toNat =\n some { name := fieldName, ty := FieldType.address } := by\n simpa [IRStorageSlot.toNat_ofNat_wordNormalize] using\n (show findResolvedFieldAtSlotCopy fields (SourceSemantics.wordNormalize slot) =\n some { name := fieldName, ty := FieldType.address } from\n by rw [findResolvedFieldAtSlotCopy_wordNormalize]; exact hresolved)\n rw [encodeStorageAt_eq_storageAddr_of_resolvedSlot hresolved' (by rfl) (by rfl)] at hIR\n set v := (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).val\n set state' := state.setVar name v\n set runtime' := { runtime with bindings := SourceSemantics.bindValue runtime.bindings name v }\n have hAddrLt : v < Verity.Core.UINT256_MODULUS :=\n Nat.lt_trans (runtime.world.storageAddr (SourceSemantics.wordNormalize slot)).isLt (by decide)\n have hNextScopeIncl : FunctionBody.scopeNamesIncluded\n (stmtNextScope scope (.assignVar name (Expr.storageAddr fieldName))) (name :: scope) := by\n intro n hn; simp [stmtNextScope, collectStmtNames, collectExprNames] at hn\n rcases hn with rfl | rfl | hn <;>\n [simp; exact List.mem_cons_of_mem _ hfieldInScope; exact List.mem_cons_of_mem _ hn]\n refine ⟨.continue runtime', .continue state', ?_, ?_, ?_⟩\n · show (match SourceSemantics.evalExpr fields runtime (.storageAddr fieldName) with\n | some r => SourceSemantics.StmtResult.continue { runtime with\n bindings := SourceSemantics.bindValue runtime.bindings name r }\n | none => SourceSemantics.StmtResult.revert) = _; rw [hEvalSrc]\n · have : [YulStmt.assign name (YulExpr.call \"sload\" [YulExpr.lit slot])].length +\n extraFuel + 1 = Nat.succ (Nat.succ extraFuel) := by simp [List.length]; omega\n rw [this]; simp [execIRStmts, execIRStmt, hIR, state', v,\n SourceSemantics.wordNormalize, Compiler.Constants.evmModulus,\n Verity.Core.UINT256_MODULUS]\n apply congrArg (state.setVar name)\n exact Nat.mod_eq_of_lt (by\n simpa [Verity.Core.UINT256_MODULUS] using hAddrLt)\n · simp only [stmtStepMatchesIRExec]\n exact ⟨FunctionBody.runtimeStateMatchesIR_setVar_bindValue hruntime name v,\n FunctionBody.bindingsExactlyMatchIRVarsOnScope_of_included\n (FunctionBody.bindingsExactlyMatchIRVarsOnScope_setVar_bindValue hexact) hNextScopeIncl,\n FunctionBody.bindingsBounded_bindValue hbounded name v hAddrLt,\n FunctionBody.scopeNamesPresent_of_included\n (FunctionBody.scopeNamesPresent_cons_bindValue hscope) hNextScopeIncl⟩\n\nprivate theorem stmtListGenericCore_singleton_setStorageAddr_singleSlot\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {slot : Nat}\n {value : Expr}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorageAddr fieldName value] := by\n rcases FunctionBody.compileExpr_core_ok (fields := fields) hcore with\n ⟨valueIR, hvalueIR⟩\n exact StmtListGenericCore.cons\n (compiledStmtStep_setStorageAddr_singleSlot\n (hcore := hcore)\n (hinScope := hinScope)\n (hfind := hfind)\n (hwriteSlots := by simpa using findFieldWriteSlots_of_findFieldWithResolvedSlot hfind)\n (hnoConflict := hnoConflict)\n (hvalueIR := hvalueIR))\n StmtListGenericCore.nil\n\ntheorem stmtListGenericCore_of_supportedStmtList_setStorageAddrSingleSlot_of_surface\n {fields : List Field}\n {scope : List String}\n {fieldName : String}\n {value : Expr}\n {slot : Nat}\n (hnoConflict : firstFieldWriteSlotConflict fields = none)\n (hfind : findFieldWithResolvedSlot fields fieldName =\n some ({ name := fieldName, ty := FieldType.address }, slot))\n (hcore : FunctionBody.ExprCompileCore value)\n (hinScope : FunctionBody.exprBoundNamesInScope value scope) :\n StmtListGenericCore fields scope [Stmt.setStorageAddr fieldName value] :=\n stmtListGenericCore_singleton_setStorageAddr_singleSlot\n (fields := fields)\n (scope := scope)\n (hnoConflict := hnoConflict)\n (hfind := hfind)\n (hcore := hcore)\n (hinScope := hinScope)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -407,6 +407,48 @@\n · simp\n · exact hih\n \n+private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n+ {seen current : List (Nat × String × Option PackedBits)}\n+ {slot : Nat}\n+ (hseen : slot ∈ seen.map (fun entry => entry.1))\n+ (hcurrent : slot ∈ current.map (fun entry => entry.1))\n+ (hunpacked : ∀ packed ∈ current.map (fun entry => entry.2.2), packed = none) :\n+ firstInFieldConflictCopy seen current ≠ none := by\n+ induction current generalizing seen with\n+ | nil =>\n+ simp at hcurrent\n+ | cons entry rest ih =>\n+ simp at hcurrent\n+ have hpnone : entry.2.2 = none := hunpacked entry.2.2 (by simp)\n+ have hunpackedRest :\n+ ∀ packed ∈ rest.map (fun restEntry => restEntry.2.2), packed = none := by\n+ intro packed hmem\n+ exact hunpacked packed (by simp [hmem])\n+ -- entry = (entry.1, entry.2.1, entry.2.2) and entry.2.2 = none\n+ obtain ⟨e1, e21, e22⟩ := entry\n+ simp at hpnone\n+ subst hpnone\n+ -- Now entry = (e1, e21, none)\n+ rcases hcurrent with ⟨rfl, _⟩ | ⟨_, _, hrest⟩\n+ · -- slot = e1\n+ have hfindSeen := list_findSlotPackedNone_ne_none hseen\n+ simp only [firstInFieldConflictCopy]\n+ cases hf : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n+ · exact absurd hf hfindSeen\n+ · simp\n+ · have hrest' : slot ∈ rest.map (fun entry => entry.1) :=\n+ List.mem_map.mpr ⟨(slot, _, _), hrest, rfl⟩\n+ intro hnone\n+ simp only [firstInFieldConflictCopy] at hnone\n+ cases hfind : seen.find? (fun seenEntry => seenEntry.1 == e1 && packedSlotsConflict seenEntry.2.2 none)\n+ · rw [hfind] at hnone\n+ simp at hnone\n+ have hseen' :\n+ slot ∈ (((e1, e21, none) :: seen).map (fun seenEntry => seenEntry.1)) := by\n+ simp [hseen]\n+ exact (ih hseen' hrest' hunpackedRest) hnone\n+ · rw [hfind] at hnone; simp at hnone\n+\n private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n@@ -423,7 +465,51 @@\n findFieldWriteSlotsCopyFrom fields idx fieldName = some writeSlots)\n (hslot : targetSlot ∈ writeSlots)\n (hunpacked : f.packedBits = none) :\n- firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := sorry\n+ firstFieldWriteSlotConflictCopyFrom seen idx fields ≠ none := by\n+ induction fields generalizing seen idx with\n+ | nil => simp [findFieldWithResolvedSlotCopyFrom] at hfind\n+ | cons field rest ih =>\n+ simp only [findFieldWithResolvedSlotCopyFrom] at hfind\n+ simp only [findFieldWriteSlotsCopyFrom] at hwrite\n+ simp only [firstFieldWriteSlotConflictCopyFrom]\n+ by_cases hname : field.name == fieldName\n+ · -- field.name matches: hfind and hwrite resolve here\n+ simp [hname] at hfind hwrite\n+ obtain ⟨rfl, rfl⟩ := hfind\n+ subst hwrite\n+ -- Need: firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) ≠ none\n+ -- targetSlot ∈ writeSlots = (field.slot.getD idx :: field.aliasSlots)\n+ -- fieldWriteEntriesAt produces entries with first components matching writeSlots\n+ -- and all packed bits = field.packedBits = none\n+ have htarget_in_entries :\n+ SourceSemantics.wordNormalize targetSlot ∈\n+ (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n+ simp only [List.mem_cons] at hslot\n+ rcases hslot with hslot | halias\n+ · subst targetSlot\n+ exact fieldWriteEntriesAt_base_mem idx field\n+ · exact fieldWriteEntriesAt_alias_mem halias\n+ have hunpacked_entries :\n+ ∀ packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry.2.2),\n+ packed = none := by\n+ intro packed hmem\n+ exact fieldWriteEntriesAt_packed_none_of_unpacked hunpacked hmem\n+ have hconflict := firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n+ hseen htarget_in_entries hunpacked_entries\n+ cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n+ | none => exact absurd hc hconflict\n+ | some _ => simp\n+ · -- field.name doesn't match: recurse\n+ simp [hname] at hfind hwrite\n+ have hseen' :\n+ SourceSemantics.wordNormalize targetSlot ∈\n+ ((fieldWriteEntriesAt idx field).reverse ++ seen).map\n+ (fun entry => entry.1) := by\n+ rw [List.map_append, List.mem_append]\n+ exact Or.inr hseen\n+ cases hc : firstInFieldConflictCopy seen (fieldWriteEntriesAt idx field) with\n+ | some _ => simp\n+ | none => exact ih hseen' hfind hwrite\n \n theorem findResolvedFieldAtSlotCopyFrom_of_member\n {fields : List Field}\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21348,"cells":{"task_id":{"kind":"string","value":"ablate_111066ac5beb_0"},"challenge_id":{"kind":"string","value":"74c8d9b10991847e"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/Core/Uint256.lean"},"theory":{"kind":"string","value":"Uint256"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":4,"string":"4"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"max_uint256_succ_eq_modulus","depth":1,"n_commands":0,"n_lines":6,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]","n_chars":265,"n_subproofs":3,"n_tactics":6,"cyclomatic":1,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":4},{"theorem_name":"sub_add_cancel_left","depth":1,"n_commands":0,"n_lines":54,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)","n_chars":1876,"n_subproofs":8,"n_tactics":53,"cyclomatic":1,"n_automation":13,"n_rewrites":0,"n_structural":13,"automation_only":false,"max_nesting":16},{"theorem_name":"sub_add_cancel_of_lt","depth":1,"n_commands":0,"n_lines":102,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''","n_chars":4153,"n_subproofs":29,"n_tactics":100,"cyclomatic":3,"n_automation":17,"n_rewrites":2,"n_structural":24,"automation_only":false,"max_nesting":20},{"theorem_name":"add_right_cancel","depth":1,"n_commands":0,"n_lines":8,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n calc\n a = a + c - c := by\n symm\n exact (sub_add_cancel a c)\n _ = b + c - c := by simp [h]\n _ = b := by\n exact (sub_add_cancel b c)","n_chars":172,"n_subproofs":0,"n_tactics":8,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"max_uint256_succ_eq_modulus\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 6,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have h2 : (0 : Nat) < (2 : Nat) := by decide\\n have hle : 1 ≤ (2 ^ 256) := by\\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\",\n \"n_chars\": 265,\n \"n_subproofs\": 3,\n \"n_tactics\": 6,\n \"cyclomatic\": 1,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n },\n {\n \"theorem_name\": \"sub_add_cancel_left\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 54,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n apply ext\\n let m : Nat := modulus\\n by_cases h : b.val ≤ a.val\\n · have hlt : a.val - b.val < m := by\\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\\n calc\\n ((a - b) + b).val\\n = (((a.val - b.val) % m) + b.val) % m := by\\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\\n _ = ((a.val - b.val) + b.val) % m := by\\n simp [Nat.mod_eq_of_lt hlt]\\n _ = a.val % m := by\\n simp [Nat.sub_add_cancel h]\\n _ = a.val := by\\n exact Nat.mod_eq_of_lt (by\\n simp [m]\\n exact a.isLt)\\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\\n let d : Nat := b.val - a.val\\n have hba : d < m := by\\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\\n have hsum : m - d + b.val = m + a.val := by\\n -- b = a + (b - a)\\n have hba_eq : b.val = a.val + d := by\\n have h' : b.val = d + a.val := by\\n symm\\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\\n calc\\n b.val = d + a.val := h'\\n _ = a.val + d := by simp [Nat.add_comm]\\n calc\\n m - d + b.val\\n = m - d + (a.val + d) := by simp [hba_eq]\\n _ = (m - d + d) + a.val := by\\n simp [Nat.add_assoc, Nat.add_comm]\\n _ = m + a.val := by\\n have hle : d ≤ m := Nat.le_of_lt hba\\n simp [Nat.sub_add_cancel hle]\\n calc\\n ((a - b) + b).val\\n = (((m - d) % m) + b.val) % m := by\\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\\n _ = ((m - d) + b.val) % m := by\\n simp\\n _ = (m + a.val) % m := by\\n simp [hsum]\\n _ = a.val % m := by\\n simp [Nat.add_mod_left]\\n _ = a.val := by\\n exact Nat.mod_eq_of_lt (by\\n simp [m]\\n exact a.isLt)\",\n \"n_chars\": 1876,\n \"n_subproofs\": 8,\n \"n_tactics\": 53,\n \"cyclomatic\": 1,\n \"n_automation\": 13,\n \"n_rewrites\": 0,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"sub_add_cancel_of_lt\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 102,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n cases a with\\n | mk a ha' =>\\n cases b with\\n | mk b hb' =>\\n apply ext\\n let m : Nat := modulus\\n have ha'' : a < m := by\\n simp [m]\\n exact ha\\n have hb'' : b < m := by\\n simp [m]\\n exact hb\\n by_cases h : a + b < m\\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\\n have hb_le' : b ≤ (a + b) % m := by\\n calc b\\n _ ≤ a + b := hb_le\\n _ = (a + b) % m := hmod.symm\\n have hb_le_modulus : b ≤ (a + b) % modulus := by\\n simpa [m] using hb_le'\\n -- No overflow: direct cancellation.\\n calc\\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\\n simp [add, sub, ofNat, hb_le_modulus, m]\\n _ = ((a + b) % m - b) % m := rfl\\n _ = (a + b - b) % m := by rw [hmod]\\n _ = a % m := by rw [Nat.add_sub_cancel]\\n _ = a := Nat.mod_eq_of_lt ha''\\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\\n have hmod : (a + b) % m = a + b - m := by\\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\\n simp [hmod', hmod'']\\n have hlt' : a + b < b + m := by\\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\\n calc\\n a + b < m + b := h'\\n _ = b + m := by\\n simp [Nat.add_comm]\\n have hbgt : b > a + b - m := by\\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\\n have hsum : (m - a) + (a + b - m) = b := by\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n calc\\n (m - a) + (a + b - m)\\n = (m - a) + (a + b) - m := by\\n symm\\n exact Nat.add_sub_assoc h_ge (m - a)\\n _ = ((m - a) + a) + b - m := by\\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\\n _ = m + b - m := by\\n simp [Nat.sub_add_cancel hma]\\n _ = b := by\\n exact Nat.add_sub_cancel_left m b\\n have hdiff : b - (a + b - m) = m - a := by\\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\\n have hbnot' : ¬ b ≤ (a + b) % m := by\\n intro hc\\n have : b ≤ a + b - m := by calc b\\n _ ≤ (a + b) % m := hc\\n _ = a + b - m := hmod\\n exact hbnot this\\n -- Overflow: wrap-around branch.\\n let aU : Uint256 := ⟨a, ha'⟩\\n let bU : Uint256 := ⟨b, hb'⟩\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n have hsub : m - (m - a) = a := by\\n have hle' : m - a ≤ m := Nat.sub_le _ _\\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\\n calc\\n m = m - a + a := h1.symm\\n _ = a + (m - a) := by\\n simp [Nat.add_comm])\\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\\n have hgt : b > (a + b) % m := by\\n exact Nat.lt_of_not_ge hbnot'\\n have hgt' : bU.val > (add aU bU).val := by\\n simp [aU, bU, add, ofNat]\\n exact hgt\\n calc\\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\\n _ = (m - (bU.val - (add aU bU).val)) % m := by\\n simp [sub_val_of_gt, hgt', m]\\n _ = (m - (b - (a + b) % m)) % m := by\\n simp [aU, bU, add, ofNat, m]\\n calc\\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\\n _ = (m - (b - (a + b - m))) % m := by\\n simp [hmod]\\n _ = (m - (m - a)) % m := by\\n simp [hdiff]\\n _ = a % m := by\\n simp [hsub]\\n _ = a := by\\n exact Nat.mod_eq_of_lt ha''\",\n \"n_chars\": 4153,\n \"n_subproofs\": 29,\n \"n_tactics\": 100,\n \"cyclomatic\": 3,\n \"n_automation\": 17,\n \"n_rewrites\": 2,\n \"n_structural\": 24,\n \"automation_only\": false,\n \"max_nesting\": 20\n },\n {\n \"theorem_name\": \"add_right_cancel\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 8,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n calc\\n a = a + c - c := by\\n symm\\n exact (sub_add_cancel a c)\\n _ = b + c - c := by simp [h]\\n _ = b := by\\n exact (sub_add_cancel b c)\",\n \"n_chars\": 172,\n \"n_subproofs\": 0,\n \"n_tactics\": 8,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"sub_add_cancel","text":"theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\n","fan_in":4,"n_lines":4,"n_chars":98,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"sub_add_cancel\",\n \"text\": \"theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\\n sub_add_cancel_of_lt a.isLt b.isLt\\n\\n\",\n \"fan_in\": 4,\n \"n_lines\": 4,\n \"n_chars\": 98,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"max_uint256_succ_eq_modulus","fan_in":1,"n_deps_direct":1,"n_deps_transitive":7,"n_lines":8,"n_chars":333,"n_subproofs":3,"n_tactics":6,"cyclomatic":1,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"max_uint256_succ_eq_modulus\",\n \"fan_in\": 1,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 7,\n \"n_lines\": 8,\n \"n_chars\": 333,\n \"n_subproofs\": 3,\n \"n_tactics\": 6,\n \"cyclomatic\": 1,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ntheorem max_uint256_succ_eq_modulus : MAX_UINT256 + 1 = modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := sorry\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · sorry\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := sorry\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := sorry\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := sorry\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\nend Uint256\n\nend Verity.Core\n"},"solution_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ntheorem max_uint256_succ_eq_modulus : MAX_UINT256 + 1 = modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\ntheorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\nend Uint256\n\nend Verity.Core\n"},"solution_diff":{"kind":"string","value":"@@ -37,7 +37,7 @@\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n- have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := sorry\n+ have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\n \n def ofNat (n : Nat) : Uint256 :=\n@@ -363,12 +363,42 @@\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n- · sorry\n+ · have hlt : a.val - b.val < m := by\n+ exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n+ have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n+ calc\n+ ((a - b) + b).val\n+ = (((a.val - b.val) % m) + b.val) % m := by\n+ simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n+ _ = ((a.val - b.val) + b.val) % m := by\n+ simp [Nat.mod_eq_of_lt hlt]\n+ _ = a.val % m := by\n+ simp [Nat.sub_add_cancel h]\n+ _ = a.val := by\n+ exact Nat.mod_eq_of_lt (by\n+ simp [m]\n+ exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n- have hsum : m - d + b.val = m + a.val := sorry\n+ have hsum : m - d + b.val = m + a.val := by\n+ -- b = a + (b - a)\n+ have hba_eq : b.val = a.val + d := by\n+ have h' : b.val = d + a.val := by\n+ symm\n+ exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n+ calc\n+ b.val = d + a.val := h'\n+ _ = a.val + d := by simp [Nat.add_comm]\n+ calc\n+ m - d + b.val\n+ = m - d + (a.val + d) := by simp [hba_eq]\n+ _ = (m - d + d) + a.val := by\n+ simp [Nat.add_assoc, Nat.add_comm]\n+ _ = m + a.val := by\n+ have hle : d ≤ m := Nat.le_of_lt hba\n+ simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n@@ -454,7 +484,19 @@\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n- have hsum : (m - a) + (a + b - m) = b := sorry\n+ have hsum : (m - a) + (a + b - m) = b := by\n+ have hma : a ≤ m := Nat.le_of_lt ha''\n+ calc\n+ (m - a) + (a + b - m)\n+ = (m - a) + (a + b) - m := by\n+ symm\n+ exact Nat.add_sub_assoc h_ge (m - a)\n+ _ = ((m - a) + a) + b - m := by\n+ simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n+ _ = m + b - m := by\n+ simp [Nat.sub_add_cancel hma]\n+ _ = b := by\n+ exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n@@ -470,7 +512,7 @@\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n- have h1 : m - a + a = m := sorry\n+ have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n@@ -498,6 +540,9 @@\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n \n+theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n+ sub_add_cancel_of_lt a.isLt b.isLt\n+\n end Uint256\n \n end Verity.Core\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21349,"cells":{"task_id":{"kind":"string","value":"ablate_111066ac5beb_1"},"challenge_id":{"kind":"string","value":"7a51c88a91b23a5a"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/Core/Uint256.lean"},"theory":{"kind":"string","value":"Uint256"},"variant":{"kind":"number","value":1,"string":"1"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":4,"string":"4"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"max_uint256_succ_eq_modulus","depth":1,"n_commands":0,"n_lines":6,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]","n_chars":265,"n_subproofs":3,"n_tactics":6,"cyclomatic":1,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":4},{"theorem_name":"sub_add_cancel_left","depth":1,"n_commands":0,"n_lines":54,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)","n_chars":1876,"n_subproofs":8,"n_tactics":53,"cyclomatic":1,"n_automation":13,"n_rewrites":0,"n_structural":13,"automation_only":false,"max_nesting":16},{"theorem_name":"sub_add_cancel_of_lt","depth":1,"n_commands":0,"n_lines":102,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''","n_chars":4153,"n_subproofs":29,"n_tactics":100,"cyclomatic":3,"n_automation":17,"n_rewrites":2,"n_structural":24,"automation_only":false,"max_nesting":20},{"theorem_name":"add_right_cancel","depth":1,"n_commands":0,"n_lines":8,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n calc\n a = a + c - c := by\n symm\n exact (sub_add_cancel a c)\n _ = b + c - c := by simp [h]\n _ = b := by\n exact (sub_add_cancel b c)","n_chars":172,"n_subproofs":0,"n_tactics":8,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"max_uint256_succ_eq_modulus\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 6,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have h2 : (0 : Nat) < (2 : Nat) := by decide\\n have hle : 1 ≤ (2 ^ 256) := by\\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\",\n \"n_chars\": 265,\n \"n_subproofs\": 3,\n \"n_tactics\": 6,\n \"cyclomatic\": 1,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n },\n {\n \"theorem_name\": \"sub_add_cancel_left\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 54,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n apply ext\\n let m : Nat := modulus\\n by_cases h : b.val ≤ a.val\\n · have hlt : a.val - b.val < m := by\\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\\n calc\\n ((a - b) + b).val\\n = (((a.val - b.val) % m) + b.val) % m := by\\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\\n _ = ((a.val - b.val) + b.val) % m := by\\n simp [Nat.mod_eq_of_lt hlt]\\n _ = a.val % m := by\\n simp [Nat.sub_add_cancel h]\\n _ = a.val := by\\n exact Nat.mod_eq_of_lt (by\\n simp [m]\\n exact a.isLt)\\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\\n let d : Nat := b.val - a.val\\n have hba : d < m := by\\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\\n have hsum : m - d + b.val = m + a.val := by\\n -- b = a + (b - a)\\n have hba_eq : b.val = a.val + d := by\\n have h' : b.val = d + a.val := by\\n symm\\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\\n calc\\n b.val = d + a.val := h'\\n _ = a.val + d := by simp [Nat.add_comm]\\n calc\\n m - d + b.val\\n = m - d + (a.val + d) := by simp [hba_eq]\\n _ = (m - d + d) + a.val := by\\n simp [Nat.add_assoc, Nat.add_comm]\\n _ = m + a.val := by\\n have hle : d ≤ m := Nat.le_of_lt hba\\n simp [Nat.sub_add_cancel hle]\\n calc\\n ((a - b) + b).val\\n = (((m - d) % m) + b.val) % m := by\\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\\n _ = ((m - d) + b.val) % m := by\\n simp\\n _ = (m + a.val) % m := by\\n simp [hsum]\\n _ = a.val % m := by\\n simp [Nat.add_mod_left]\\n _ = a.val := by\\n exact Nat.mod_eq_of_lt (by\\n simp [m]\\n exact a.isLt)\",\n \"n_chars\": 1876,\n \"n_subproofs\": 8,\n \"n_tactics\": 53,\n \"cyclomatic\": 1,\n \"n_automation\": 13,\n \"n_rewrites\": 0,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"sub_add_cancel_of_lt\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 102,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n cases a with\\n | mk a ha' =>\\n cases b with\\n | mk b hb' =>\\n apply ext\\n let m : Nat := modulus\\n have ha'' : a < m := by\\n simp [m]\\n exact ha\\n have hb'' : b < m := by\\n simp [m]\\n exact hb\\n by_cases h : a + b < m\\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\\n have hb_le' : b ≤ (a + b) % m := by\\n calc b\\n _ ≤ a + b := hb_le\\n _ = (a + b) % m := hmod.symm\\n have hb_le_modulus : b ≤ (a + b) % modulus := by\\n simpa [m] using hb_le'\\n -- No overflow: direct cancellation.\\n calc\\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\\n simp [add, sub, ofNat, hb_le_modulus, m]\\n _ = ((a + b) % m - b) % m := rfl\\n _ = (a + b - b) % m := by rw [hmod]\\n _ = a % m := by rw [Nat.add_sub_cancel]\\n _ = a := Nat.mod_eq_of_lt ha''\\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\\n have hmod : (a + b) % m = a + b - m := by\\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\\n simp [hmod', hmod'']\\n have hlt' : a + b < b + m := by\\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\\n calc\\n a + b < m + b := h'\\n _ = b + m := by\\n simp [Nat.add_comm]\\n have hbgt : b > a + b - m := by\\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\\n have hsum : (m - a) + (a + b - m) = b := by\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n calc\\n (m - a) + (a + b - m)\\n = (m - a) + (a + b) - m := by\\n symm\\n exact Nat.add_sub_assoc h_ge (m - a)\\n _ = ((m - a) + a) + b - m := by\\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\\n _ = m + b - m := by\\n simp [Nat.sub_add_cancel hma]\\n _ = b := by\\n exact Nat.add_sub_cancel_left m b\\n have hdiff : b - (a + b - m) = m - a := by\\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\\n have hbnot' : ¬ b ≤ (a + b) % m := by\\n intro hc\\n have : b ≤ a + b - m := by calc b\\n _ ≤ (a + b) % m := hc\\n _ = a + b - m := hmod\\n exact hbnot this\\n -- Overflow: wrap-around branch.\\n let aU : Uint256 := ⟨a, ha'⟩\\n let bU : Uint256 := ⟨b, hb'⟩\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n have hsub : m - (m - a) = a := by\\n have hle' : m - a ≤ m := Nat.sub_le _ _\\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\\n calc\\n m = m - a + a := h1.symm\\n _ = a + (m - a) := by\\n simp [Nat.add_comm])\\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\\n have hgt : b > (a + b) % m := by\\n exact Nat.lt_of_not_ge hbnot'\\n have hgt' : bU.val > (add aU bU).val := by\\n simp [aU, bU, add, ofNat]\\n exact hgt\\n calc\\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\\n _ = (m - (bU.val - (add aU bU).val)) % m := by\\n simp [sub_val_of_gt, hgt', m]\\n _ = (m - (b - (a + b) % m)) % m := by\\n simp [aU, bU, add, ofNat, m]\\n calc\\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\\n _ = (m - (b - (a + b - m))) % m := by\\n simp [hmod]\\n _ = (m - (m - a)) % m := by\\n simp [hdiff]\\n _ = a % m := by\\n simp [hsub]\\n _ = a := by\\n exact Nat.mod_eq_of_lt ha''\",\n \"n_chars\": 4153,\n \"n_subproofs\": 29,\n \"n_tactics\": 100,\n \"cyclomatic\": 3,\n \"n_automation\": 17,\n \"n_rewrites\": 2,\n \"n_structural\": 24,\n \"automation_only\": false,\n \"max_nesting\": 20\n },\n {\n \"theorem_name\": \"add_right_cancel\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 8,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n calc\\n a = a + c - c := by\\n symm\\n exact (sub_add_cancel a c)\\n _ = b + c - c := by simp [h]\\n _ = b := by\\n exact (sub_add_cancel b c)\",\n \"n_chars\": 172,\n \"n_subproofs\": 0,\n \"n_tactics\": 8,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"sub_add_cancel","text":"theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\n","fan_in":4,"n_lines":4,"n_chars":98,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"sub_add_cancel\",\n \"text\": \"theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\\n sub_add_cancel_of_lt a.isLt b.isLt\\n\\n\",\n \"fan_in\": 4,\n \"n_lines\": 4,\n \"n_chars\": 98,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"val_le_max","fan_in":0,"n_deps_direct":1,"n_deps_transitive":8,"n_lines":11,"n_chars":304,"n_subproofs":2,"n_tactics":9,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"val_le_max\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 8,\n \"n_lines\": 11,\n \"n_chars\": 304,\n \"n_subproofs\": 2,\n \"n_tactics\": 9,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":4,"string":"4"},"challenge_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ntheorem max_uint256_succ_eq_modulus : MAX_UINT256 + 1 = modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := sorry\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\n\ntheorem val_le_max (a : Uint256) : a.val ≤ MAX_UINT256 := by\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val < MAX_UINT256 + 1 := by\n calc\n a.val < modulus := hlt\n _ = MAX_UINT256 + 1 := by\n symm\n exact max_uint256_succ_eq_modulus\n exact Nat.lt_succ_iff.mp hlt'\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · sorry\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := sorry\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := sorry\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := sorry\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\nend Uint256\n\nend Verity.Core\n"},"solution_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ntheorem max_uint256_succ_eq_modulus : MAX_UINT256 + 1 = modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\n\ntheorem val_le_max (a : Uint256) : a.val ≤ MAX_UINT256 := by\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val < MAX_UINT256 + 1 := by\n calc\n a.val < modulus := hlt\n _ = MAX_UINT256 + 1 := by\n symm\n exact max_uint256_succ_eq_modulus\n exact Nat.lt_succ_iff.mp hlt'\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\ntheorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\nend Uint256\n\nend Verity.Core\n"},"solution_diff":{"kind":"string","value":"@@ -37,7 +37,7 @@\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n- have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := sorry\n+ have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\n \n theorem val_le_max (a : Uint256) : a.val ≤ MAX_UINT256 := by\n@@ -373,12 +373,42 @@\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n- · sorry\n+ · have hlt : a.val - b.val < m := by\n+ exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n+ have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n+ calc\n+ ((a - b) + b).val\n+ = (((a.val - b.val) % m) + b.val) % m := by\n+ simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n+ _ = ((a.val - b.val) + b.val) % m := by\n+ simp [Nat.mod_eq_of_lt hlt]\n+ _ = a.val % m := by\n+ simp [Nat.sub_add_cancel h]\n+ _ = a.val := by\n+ exact Nat.mod_eq_of_lt (by\n+ simp [m]\n+ exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n- have hsum : m - d + b.val = m + a.val := sorry\n+ have hsum : m - d + b.val = m + a.val := by\n+ -- b = a + (b - a)\n+ have hba_eq : b.val = a.val + d := by\n+ have h' : b.val = d + a.val := by\n+ symm\n+ exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n+ calc\n+ b.val = d + a.val := h'\n+ _ = a.val + d := by simp [Nat.add_comm]\n+ calc\n+ m - d + b.val\n+ = m - d + (a.val + d) := by simp [hba_eq]\n+ _ = (m - d + d) + a.val := by\n+ simp [Nat.add_assoc, Nat.add_comm]\n+ _ = m + a.val := by\n+ have hle : d ≤ m := Nat.le_of_lt hba\n+ simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n@@ -464,7 +494,19 @@\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n- have hsum : (m - a) + (a + b - m) = b := sorry\n+ have hsum : (m - a) + (a + b - m) = b := by\n+ have hma : a ≤ m := Nat.le_of_lt ha''\n+ calc\n+ (m - a) + (a + b - m)\n+ = (m - a) + (a + b) - m := by\n+ symm\n+ exact Nat.add_sub_assoc h_ge (m - a)\n+ _ = ((m - a) + a) + b - m := by\n+ simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n+ _ = m + b - m := by\n+ simp [Nat.sub_add_cancel hma]\n+ _ = b := by\n+ exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n@@ -480,7 +522,7 @@\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n- have h1 : m - a + a = m := sorry\n+ have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n@@ -508,6 +550,9 @@\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n \n+theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n+ sub_add_cancel_of_lt a.isLt b.isLt\n+\n end Uint256\n \n end Verity.Core\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21350,"cells":{"task_id":{"kind":"string","value":"ablate_111066ac5beb_2"},"challenge_id":{"kind":"string","value":"487b7f86647800b3"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/Core/Uint256.lean"},"theory":{"kind":"string","value":"Uint256"},"variant":{"kind":"number","value":2,"string":"2"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":4,"string":"4"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"max_uint256_succ_eq_modulus","depth":1,"n_commands":0,"n_lines":6,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]","n_chars":265,"n_subproofs":3,"n_tactics":6,"cyclomatic":1,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":4},{"theorem_name":"sub_add_cancel_left","depth":1,"n_commands":0,"n_lines":54,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)","n_chars":1876,"n_subproofs":8,"n_tactics":53,"cyclomatic":1,"n_automation":13,"n_rewrites":0,"n_structural":13,"automation_only":false,"max_nesting":16},{"theorem_name":"sub_add_cancel_of_lt","depth":1,"n_commands":0,"n_lines":102,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''","n_chars":4153,"n_subproofs":29,"n_tactics":100,"cyclomatic":3,"n_automation":17,"n_rewrites":2,"n_structural":24,"automation_only":false,"max_nesting":20},{"theorem_name":"add_right_cancel","depth":1,"n_commands":0,"n_lines":8,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n calc\n a = a + c - c := by\n symm\n exact (sub_add_cancel a c)\n _ = b + c - c := by simp [h]\n _ = b := by\n exact (sub_add_cancel b c)","n_chars":172,"n_subproofs":0,"n_tactics":8,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"max_uint256_succ_eq_modulus\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 6,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have h2 : (0 : Nat) < (2 : Nat) := by decide\\n have hle : 1 ≤ (2 ^ 256) := by\\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\",\n \"n_chars\": 265,\n \"n_subproofs\": 3,\n \"n_tactics\": 6,\n \"cyclomatic\": 1,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n },\n {\n \"theorem_name\": \"sub_add_cancel_left\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 54,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n apply ext\\n let m : Nat := modulus\\n by_cases h : b.val ≤ a.val\\n · have hlt : a.val - b.val < m := by\\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\\n calc\\n ((a - b) + b).val\\n = (((a.val - b.val) % m) + b.val) % m := by\\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\\n _ = ((a.val - b.val) + b.val) % m := by\\n simp [Nat.mod_eq_of_lt hlt]\\n _ = a.val % m := by\\n simp [Nat.sub_add_cancel h]\\n _ = a.val := by\\n exact Nat.mod_eq_of_lt (by\\n simp [m]\\n exact a.isLt)\\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\\n let d : Nat := b.val - a.val\\n have hba : d < m := by\\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\\n have hsum : m - d + b.val = m + a.val := by\\n -- b = a + (b - a)\\n have hba_eq : b.val = a.val + d := by\\n have h' : b.val = d + a.val := by\\n symm\\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\\n calc\\n b.val = d + a.val := h'\\n _ = a.val + d := by simp [Nat.add_comm]\\n calc\\n m - d + b.val\\n = m - d + (a.val + d) := by simp [hba_eq]\\n _ = (m - d + d) + a.val := by\\n simp [Nat.add_assoc, Nat.add_comm]\\n _ = m + a.val := by\\n have hle : d ≤ m := Nat.le_of_lt hba\\n simp [Nat.sub_add_cancel hle]\\n calc\\n ((a - b) + b).val\\n = (((m - d) % m) + b.val) % m := by\\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\\n _ = ((m - d) + b.val) % m := by\\n simp\\n _ = (m + a.val) % m := by\\n simp [hsum]\\n _ = a.val % m := by\\n simp [Nat.add_mod_left]\\n _ = a.val := by\\n exact Nat.mod_eq_of_lt (by\\n simp [m]\\n exact a.isLt)\",\n \"n_chars\": 1876,\n \"n_subproofs\": 8,\n \"n_tactics\": 53,\n \"cyclomatic\": 1,\n \"n_automation\": 13,\n \"n_rewrites\": 0,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"sub_add_cancel_of_lt\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 102,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n cases a with\\n | mk a ha' =>\\n cases b with\\n | mk b hb' =>\\n apply ext\\n let m : Nat := modulus\\n have ha'' : a < m := by\\n simp [m]\\n exact ha\\n have hb'' : b < m := by\\n simp [m]\\n exact hb\\n by_cases h : a + b < m\\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\\n have hb_le' : b ≤ (a + b) % m := by\\n calc b\\n _ ≤ a + b := hb_le\\n _ = (a + b) % m := hmod.symm\\n have hb_le_modulus : b ≤ (a + b) % modulus := by\\n simpa [m] using hb_le'\\n -- No overflow: direct cancellation.\\n calc\\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\\n simp [add, sub, ofNat, hb_le_modulus, m]\\n _ = ((a + b) % m - b) % m := rfl\\n _ = (a + b - b) % m := by rw [hmod]\\n _ = a % m := by rw [Nat.add_sub_cancel]\\n _ = a := Nat.mod_eq_of_lt ha''\\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\\n have hmod : (a + b) % m = a + b - m := by\\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\\n simp [hmod', hmod'']\\n have hlt' : a + b < b + m := by\\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\\n calc\\n a + b < m + b := h'\\n _ = b + m := by\\n simp [Nat.add_comm]\\n have hbgt : b > a + b - m := by\\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\\n have hsum : (m - a) + (a + b - m) = b := by\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n calc\\n (m - a) + (a + b - m)\\n = (m - a) + (a + b) - m := by\\n symm\\n exact Nat.add_sub_assoc h_ge (m - a)\\n _ = ((m - a) + a) + b - m := by\\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\\n _ = m + b - m := by\\n simp [Nat.sub_add_cancel hma]\\n _ = b := by\\n exact Nat.add_sub_cancel_left m b\\n have hdiff : b - (a + b - m) = m - a := by\\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\\n have hbnot' : ¬ b ≤ (a + b) % m := by\\n intro hc\\n have : b ≤ a + b - m := by calc b\\n _ ≤ (a + b) % m := hc\\n _ = a + b - m := hmod\\n exact hbnot this\\n -- Overflow: wrap-around branch.\\n let aU : Uint256 := ⟨a, ha'⟩\\n let bU : Uint256 := ⟨b, hb'⟩\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n have hsub : m - (m - a) = a := by\\n have hle' : m - a ≤ m := Nat.sub_le _ _\\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\\n calc\\n m = m - a + a := h1.symm\\n _ = a + (m - a) := by\\n simp [Nat.add_comm])\\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\\n have hgt : b > (a + b) % m := by\\n exact Nat.lt_of_not_ge hbnot'\\n have hgt' : bU.val > (add aU bU).val := by\\n simp [aU, bU, add, ofNat]\\n exact hgt\\n calc\\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\\n _ = (m - (bU.val - (add aU bU).val)) % m := by\\n simp [sub_val_of_gt, hgt', m]\\n _ = (m - (b - (a + b) % m)) % m := by\\n simp [aU, bU, add, ofNat, m]\\n calc\\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\\n _ = (m - (b - (a + b - m))) % m := by\\n simp [hmod]\\n _ = (m - (m - a)) % m := by\\n simp [hdiff]\\n _ = a % m := by\\n simp [hsub]\\n _ = a := by\\n exact Nat.mod_eq_of_lt ha''\",\n \"n_chars\": 4153,\n \"n_subproofs\": 29,\n \"n_tactics\": 100,\n \"cyclomatic\": 3,\n \"n_automation\": 17,\n \"n_rewrites\": 2,\n \"n_structural\": 24,\n \"automation_only\": false,\n \"max_nesting\": 20\n },\n {\n \"theorem_name\": \"add_right_cancel\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 8,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n calc\\n a = a + c - c := by\\n symm\\n exact (sub_add_cancel a c)\\n _ = b + c - c := by simp [h]\\n _ = b := by\\n exact (sub_add_cancel b c)\",\n \"n_chars\": 172,\n \"n_subproofs\": 0,\n \"n_tactics\": 8,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"sub_add_cancel","text":"theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\n","fan_in":4,"n_lines":4,"n_chars":98,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"sub_add_cancel\",\n \"text\": \"theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\\n sub_add_cancel_of_lt a.isLt b.isLt\\n\\n\",\n \"fan_in\": 4,\n \"n_lines\": 4,\n \"n_chars\": 98,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"sub_add_cancel_left","fan_in":0,"n_deps_direct":4,"n_deps_transitive":7,"n_lines":56,"n_chars":1950,"n_subproofs":8,"n_tactics":53,"cyclomatic":1,"n_automation":13,"n_rewrites":0,"n_structural":13,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"sub_add_cancel_left\",\n \"fan_in\": 0,\n \"n_deps_direct\": 4,\n \"n_deps_transitive\": 7,\n \"n_lines\": 56,\n \"n_chars\": 1950,\n \"n_subproofs\": 8,\n \"n_tactics\": 53,\n \"cyclomatic\": 1,\n \"n_automation\": 13,\n \"n_rewrites\": 0,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · sorry\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := sorry\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := sorry\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := sorry\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\nend Uint256\n\nend Verity.Core\n"},"solution_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\ntheorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\nend Uint256\n\nend Verity.Core\n"},"solution_diff":{"kind":"string","value":"@@ -356,12 +356,42 @@\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n- · sorry\n+ · have hlt : a.val - b.val < m := by\n+ exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n+ have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n+ calc\n+ ((a - b) + b).val\n+ = (((a.val - b.val) % m) + b.val) % m := by\n+ simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n+ _ = ((a.val - b.val) + b.val) % m := by\n+ simp [Nat.mod_eq_of_lt hlt]\n+ _ = a.val % m := by\n+ simp [Nat.sub_add_cancel h]\n+ _ = a.val := by\n+ exact Nat.mod_eq_of_lt (by\n+ simp [m]\n+ exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n- have hsum : m - d + b.val = m + a.val := sorry\n+ have hsum : m - d + b.val = m + a.val := by\n+ -- b = a + (b - a)\n+ have hba_eq : b.val = a.val + d := by\n+ have h' : b.val = d + a.val := by\n+ symm\n+ exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n+ calc\n+ b.val = d + a.val := h'\n+ _ = a.val + d := by simp [Nat.add_comm]\n+ calc\n+ m - d + b.val\n+ = m - d + (a.val + d) := by simp [hba_eq]\n+ _ = (m - d + d) + a.val := by\n+ simp [Nat.add_assoc, Nat.add_comm]\n+ _ = m + a.val := by\n+ have hle : d ≤ m := Nat.le_of_lt hba\n+ simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n@@ -447,7 +477,19 @@\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n- have hsum : (m - a) + (a + b - m) = b := sorry\n+ have hsum : (m - a) + (a + b - m) = b := by\n+ have hma : a ≤ m := Nat.le_of_lt ha''\n+ calc\n+ (m - a) + (a + b - m)\n+ = (m - a) + (a + b) - m := by\n+ symm\n+ exact Nat.add_sub_assoc h_ge (m - a)\n+ _ = ((m - a) + a) + b - m := by\n+ simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n+ _ = m + b - m := by\n+ simp [Nat.sub_add_cancel hma]\n+ _ = b := by\n+ exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n@@ -463,7 +505,7 @@\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n- have h1 : m - a + a = m := sorry\n+ have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n@@ -491,6 +533,9 @@\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n \n+theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n+ sub_add_cancel_of_lt a.isLt b.isLt\n+\n end Uint256\n \n end Verity.Core\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21351,"cells":{"task_id":{"kind":"string","value":"ablate_111066ac5beb_3"},"challenge_id":{"kind":"string","value":"e6bf01f1093df4cb"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/Core/Uint256.lean"},"theory":{"kind":"string","value":"Uint256"},"variant":{"kind":"number","value":3,"string":"3"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"sub_add_cancel","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n sub_add_cancel_of_lt a.isLt b.isLt","n_chars":37,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"sub_add_cancel\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n sub_add_cancel_of_lt a.isLt b.isLt\",\n \"n_chars\": 37,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"sub_add_cancel_of_lt","text":"theorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\n","fan_in":1,"n_lines":105,"n_chars":4268,"n_subproofs":29,"n_tactics":100,"cyclomatic":3,"n_automation":17,"n_rewrites":2,"n_structural":24,"automation_only":false,"max_nesting":20}],"string":"[\n {\n \"name\": \"sub_add_cancel_of_lt\",\n \"text\": \"theorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\\n (a + b - b) = a := by\\n cases a with\\n | mk a ha' =>\\n cases b with\\n | mk b hb' =>\\n apply ext\\n let m : Nat := modulus\\n have ha'' : a < m := by\\n simp [m]\\n exact ha\\n have hb'' : b < m := by\\n simp [m]\\n exact hb\\n by_cases h : a + b < m\\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\\n have hb_le' : b ≤ (a + b) % m := by\\n calc b\\n _ ≤ a + b := hb_le\\n _ = (a + b) % m := hmod.symm\\n have hb_le_modulus : b ≤ (a + b) % modulus := by\\n simpa [m] using hb_le'\\n -- No overflow: direct cancellation.\\n calc\\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\\n simp [add, sub, ofNat, hb_le_modulus, m]\\n _ = ((a + b) % m - b) % m := rfl\\n _ = (a + b - b) % m := by rw [hmod]\\n _ = a % m := by rw [Nat.add_sub_cancel]\\n _ = a := Nat.mod_eq_of_lt ha''\\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\\n have hmod : (a + b) % m = a + b - m := by\\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\\n simp [hmod', hmod'']\\n have hlt' : a + b < b + m := by\\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\\n calc\\n a + b < m + b := h'\\n _ = b + m := by\\n simp [Nat.add_comm]\\n have hbgt : b > a + b - m := by\\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\\n have hsum : (m - a) + (a + b - m) = b := by\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n calc\\n (m - a) + (a + b - m)\\n = (m - a) + (a + b) - m := by\\n symm\\n exact Nat.add_sub_assoc h_ge (m - a)\\n _ = ((m - a) + a) + b - m := by\\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\\n _ = m + b - m := by\\n simp [Nat.sub_add_cancel hma]\\n _ = b := by\\n exact Nat.add_sub_cancel_left m b\\n have hdiff : b - (a + b - m) = m - a := by\\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\\n have hbnot' : ¬ b ≤ (a + b) % m := by\\n intro hc\\n have : b ≤ a + b - m := by calc b\\n _ ≤ (a + b) % m := hc\\n _ = a + b - m := hmod\\n exact hbnot this\\n -- Overflow: wrap-around branch.\\n let aU : Uint256 := ⟨a, ha'⟩\\n let bU : Uint256 := ⟨b, hb'⟩\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n have hsub : m - (m - a) = a := by\\n have hle' : m - a ≤ m := Nat.sub_le _ _\\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\\n calc\\n m = m - a + a := h1.symm\\n _ = a + (m - a) := by\\n simp [Nat.add_comm])\\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\\n have hgt : b > (a + b) % m := by\\n exact Nat.lt_of_not_ge hbnot'\\n have hgt' : bU.val > (add aU bU).val := by\\n simp [aU, bU, add, ofNat]\\n exact hgt\\n calc\\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\\n _ = (m - (bU.val - (add aU bU).val)) % m := by\\n simp [sub_val_of_gt, hgt', m]\\n _ = (m - (b - (a + b) % m)) % m := by\\n simp [aU, bU, add, ofNat, m]\\n calc\\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\\n _ = (m - (b - (a + b - m))) % m := by\\n simp [hmod]\\n _ = (m - (m - a)) % m := by\\n simp [hdiff]\\n _ = a % m := by\\n simp [hsub]\\n _ = a := by\\n exact Nat.mod_eq_of_lt ha''\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 105,\n \"n_chars\": 4268,\n \"n_subproofs\": 29,\n \"n_tactics\": 100,\n \"cyclomatic\": 3,\n \"n_automation\": 17,\n \"n_rewrites\": 2,\n \"n_structural\": 24,\n \"automation_only\": false,\n \"max_nesting\": 20\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"sub_add_cancel","fan_in":4,"n_deps_direct":1,"n_deps_transitive":7,"n_lines":4,"n_chars":98,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"sub_add_cancel\",\n \"fan_in\": 4,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 7,\n \"n_lines\": 4,\n \"n_chars\": 98,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel (a b : Uint256) : (a + b - b) = a := sorry\n\nend Uint256\n\nend Verity.Core\n"},"solution_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\ntheorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\nend Uint256\n\nend Verity.Core\n"},"solution_diff":{"kind":"string","value":"@@ -429,8 +429,113 @@\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n \n-theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a := sorry\n+theorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n+ (a + b - b) = a := by\n+ cases a with\n+ | mk a ha' =>\n+ cases b with\n+ | mk b hb' =>\n+ apply ext\n+ let m : Nat := modulus\n+ have ha'' : a < m := by\n+ simp [m]\n+ exact ha\n+ have hb'' : b < m := by\n+ simp [m]\n+ exact hb\n+ by_cases h : a + b < m\n+ · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n+ have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n+ have hb_le' : b ≤ (a + b) % m := by\n+ calc b\n+ _ ≤ a + b := hb_le\n+ _ = (a + b) % m := hmod.symm\n+ have hb_le_modulus : b ≤ (a + b) % modulus := by\n+ simpa [m] using hb_le'\n+ -- No overflow: direct cancellation.\n+ calc\n+ (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n+ simp [add, sub, ofNat, hb_le_modulus, m]\n+ _ = ((a + b) % m - b) % m := rfl\n+ _ = (a + b - b) % m := by rw [hmod]\n+ _ = a % m := by rw [Nat.add_sub_cancel]\n+ _ = a := Nat.mod_eq_of_lt ha''\n+ · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n+ have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n+ have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n+ have hmod : (a + b) % m = a + b - m := by\n+ have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n+ have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n+ simp [hmod', hmod'']\n+ have hlt' : a + b < b + m := by\n+ have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n+ calc\n+ a + b < m + b := h'\n+ _ = b + m := by\n+ simp [Nat.add_comm]\n+ have hbgt : b > a + b - m := by\n+ exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n+ have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n+ have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n+ have hsum : (m - a) + (a + b - m) = b := by\n+ have hma : a ≤ m := Nat.le_of_lt ha''\n+ calc\n+ (m - a) + (a + b - m)\n+ = (m - a) + (a + b) - m := by\n+ symm\n+ exact Nat.add_sub_assoc h_ge (m - a)\n+ _ = ((m - a) + a) + b - m := by\n+ simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n+ _ = m + b - m := by\n+ simp [Nat.sub_add_cancel hma]\n+ _ = b := by\n+ exact Nat.add_sub_cancel_left m b\n+ have hdiff : b - (a + b - m) = m - a := by\n+ exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n+ have hbnot' : ¬ b ≤ (a + b) % m := by\n+ intro hc\n+ have : b ≤ a + b - m := by calc b\n+ _ ≤ (a + b) % m := hc\n+ _ = a + b - m := hmod\n+ exact hbnot this\n+ -- Overflow: wrap-around branch.\n+ let aU : Uint256 := ⟨a, ha'⟩\n+ let bU : Uint256 := ⟨b, hb'⟩\n+ have hma : a ≤ m := Nat.le_of_lt ha''\n+ have hsub : m - (m - a) = a := by\n+ have hle' : m - a ≤ m := Nat.sub_le _ _\n+ exact (Nat.sub_eq_iff_eq_add hle').2 (by\n+ have h1 : m - a + a = m := Nat.sub_add_cancel hma\n+ calc\n+ m = m - a + a := h1.symm\n+ _ = a + (m - a) := by\n+ simp [Nat.add_comm])\n+ have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n+ have hgt : b > (a + b) % m := by\n+ exact Nat.lt_of_not_ge hbnot'\n+ have hgt' : bU.val > (add aU bU).val := by\n+ simp [aU, bU, add, ofNat]\n+ exact hgt\n+ calc\n+ (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n+ _ = (m - (bU.val - (add aU bU).val)) % m := by\n+ simp [sub_val_of_gt, hgt', m]\n+ _ = (m - (b - (a + b) % m)) % m := by\n+ simp [aU, bU, add, ofNat, m]\n+ calc\n+ (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n+ _ = (m - (b - (a + b - m))) % m := by\n+ simp [hmod]\n+ _ = (m - (m - a)) % m := by\n+ simp [hdiff]\n+ _ = a % m := by\n+ simp [hsub]\n+ _ = a := by\n+ exact Nat.mod_eq_of_lt ha''\n \n+theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n+ sub_add_cancel_of_lt a.isLt b.isLt\n+\n end Uint256\n \n end Verity.Core\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21352,"cells":{"task_id":{"kind":"string","value":"ablate_111066ac5beb_4"},"challenge_id":{"kind":"string","value":"bb4e449acdf0b724"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/Core/Uint256.lean"},"theory":{"kind":"string","value":"Uint256"},"variant":{"kind":"number","value":4,"string":"4"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":4,"string":"4"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"max_uint256_succ_eq_modulus","depth":1,"n_commands":0,"n_lines":6,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]","n_chars":265,"n_subproofs":3,"n_tactics":6,"cyclomatic":1,"n_automation":2,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":4},{"theorem_name":"sub_add_cancel_left","depth":1,"n_commands":0,"n_lines":54,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)","n_chars":1876,"n_subproofs":8,"n_tactics":53,"cyclomatic":1,"n_automation":13,"n_rewrites":0,"n_structural":13,"automation_only":false,"max_nesting":16},{"theorem_name":"sub_add_cancel_of_lt","depth":1,"n_commands":0,"n_lines":102,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''","n_chars":4153,"n_subproofs":29,"n_tactics":100,"cyclomatic":3,"n_automation":17,"n_rewrites":2,"n_structural":24,"automation_only":false,"max_nesting":20},{"theorem_name":"add_right_cancel","depth":1,"n_commands":0,"n_lines":8,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n calc\n a = a + c - c := by\n symm\n exact (sub_add_cancel a c)\n _ = b + c - c := by simp [h]\n _ = b := by\n exact (sub_add_cancel b c)","n_chars":172,"n_subproofs":0,"n_tactics":8,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"max_uint256_succ_eq_modulus\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 6,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have h2 : (0 : Nat) < (2 : Nat) := by decide\\n have hle : 1 ≤ (2 ^ 256) := by\\n exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)\\n have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle\\n simp [MAX_UINT256, modulus, UINT256_MODULUS, h]\",\n \"n_chars\": 265,\n \"n_subproofs\": 3,\n \"n_tactics\": 6,\n \"cyclomatic\": 1,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n },\n {\n \"theorem_name\": \"sub_add_cancel_left\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 54,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n apply ext\\n let m : Nat := modulus\\n by_cases h : b.val ≤ a.val\\n · have hlt : a.val - b.val < m := by\\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\\n calc\\n ((a - b) + b).val\\n = (((a.val - b.val) % m) + b.val) % m := by\\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\\n _ = ((a.val - b.val) + b.val) % m := by\\n simp [Nat.mod_eq_of_lt hlt]\\n _ = a.val % m := by\\n simp [Nat.sub_add_cancel h]\\n _ = a.val := by\\n exact Nat.mod_eq_of_lt (by\\n simp [m]\\n exact a.isLt)\\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\\n let d : Nat := b.val - a.val\\n have hba : d < m := by\\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\\n have hsum : m - d + b.val = m + a.val := by\\n -- b = a + (b - a)\\n have hba_eq : b.val = a.val + d := by\\n have h' : b.val = d + a.val := by\\n symm\\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\\n calc\\n b.val = d + a.val := h'\\n _ = a.val + d := by simp [Nat.add_comm]\\n calc\\n m - d + b.val\\n = m - d + (a.val + d) := by simp [hba_eq]\\n _ = (m - d + d) + a.val := by\\n simp [Nat.add_assoc, Nat.add_comm]\\n _ = m + a.val := by\\n have hle : d ≤ m := Nat.le_of_lt hba\\n simp [Nat.sub_add_cancel hle]\\n calc\\n ((a - b) + b).val\\n = (((m - d) % m) + b.val) % m := by\\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\\n _ = ((m - d) + b.val) % m := by\\n simp\\n _ = (m + a.val) % m := by\\n simp [hsum]\\n _ = a.val % m := by\\n simp [Nat.add_mod_left]\\n _ = a.val := by\\n exact Nat.mod_eq_of_lt (by\\n simp [m]\\n exact a.isLt)\",\n \"n_chars\": 1876,\n \"n_subproofs\": 8,\n \"n_tactics\": 53,\n \"cyclomatic\": 1,\n \"n_automation\": 13,\n \"n_rewrites\": 0,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"sub_add_cancel_of_lt\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 102,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n cases a with\\n | mk a ha' =>\\n cases b with\\n | mk b hb' =>\\n apply ext\\n let m : Nat := modulus\\n have ha'' : a < m := by\\n simp [m]\\n exact ha\\n have hb'' : b < m := by\\n simp [m]\\n exact hb\\n by_cases h : a + b < m\\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\\n have hb_le' : b ≤ (a + b) % m := by\\n calc b\\n _ ≤ a + b := hb_le\\n _ = (a + b) % m := hmod.symm\\n have hb_le_modulus : b ≤ (a + b) % modulus := by\\n simpa [m] using hb_le'\\n -- No overflow: direct cancellation.\\n calc\\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\\n simp [add, sub, ofNat, hb_le_modulus, m]\\n _ = ((a + b) % m - b) % m := rfl\\n _ = (a + b - b) % m := by rw [hmod]\\n _ = a % m := by rw [Nat.add_sub_cancel]\\n _ = a := Nat.mod_eq_of_lt ha''\\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\\n have hmod : (a + b) % m = a + b - m := by\\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\\n simp [hmod', hmod'']\\n have hlt' : a + b < b + m := by\\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\\n calc\\n a + b < m + b := h'\\n _ = b + m := by\\n simp [Nat.add_comm]\\n have hbgt : b > a + b - m := by\\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\\n have hsum : (m - a) + (a + b - m) = b := by\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n calc\\n (m - a) + (a + b - m)\\n = (m - a) + (a + b) - m := by\\n symm\\n exact Nat.add_sub_assoc h_ge (m - a)\\n _ = ((m - a) + a) + b - m := by\\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\\n _ = m + b - m := by\\n simp [Nat.sub_add_cancel hma]\\n _ = b := by\\n exact Nat.add_sub_cancel_left m b\\n have hdiff : b - (a + b - m) = m - a := by\\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\\n have hbnot' : ¬ b ≤ (a + b) % m := by\\n intro hc\\n have : b ≤ a + b - m := by calc b\\n _ ≤ (a + b) % m := hc\\n _ = a + b - m := hmod\\n exact hbnot this\\n -- Overflow: wrap-around branch.\\n let aU : Uint256 := ⟨a, ha'⟩\\n let bU : Uint256 := ⟨b, hb'⟩\\n have hma : a ≤ m := Nat.le_of_lt ha''\\n have hsub : m - (m - a) = a := by\\n have hle' : m - a ≤ m := Nat.sub_le _ _\\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\\n calc\\n m = m - a + a := h1.symm\\n _ = a + (m - a) := by\\n simp [Nat.add_comm])\\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\\n have hgt : b > (a + b) % m := by\\n exact Nat.lt_of_not_ge hbnot'\\n have hgt' : bU.val > (add aU bU).val := by\\n simp [aU, bU, add, ofNat]\\n exact hgt\\n calc\\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\\n _ = (m - (bU.val - (add aU bU).val)) % m := by\\n simp [sub_val_of_gt, hgt', m]\\n _ = (m - (b - (a + b) % m)) % m := by\\n simp [aU, bU, add, ofNat, m]\\n calc\\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\\n _ = (m - (b - (a + b - m))) % m := by\\n simp [hmod]\\n _ = (m - (m - a)) % m := by\\n simp [hdiff]\\n _ = a % m := by\\n simp [hsub]\\n _ = a := by\\n exact Nat.mod_eq_of_lt ha''\",\n \"n_chars\": 4153,\n \"n_subproofs\": 29,\n \"n_tactics\": 100,\n \"cyclomatic\": 3,\n \"n_automation\": 17,\n \"n_rewrites\": 2,\n \"n_structural\": 24,\n \"automation_only\": false,\n \"max_nesting\": 20\n },\n {\n \"theorem_name\": \"add_right_cancel\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 8,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n calc\\n a = a + c - c := by\\n symm\\n exact (sub_add_cancel a c)\\n _ = b + c - c := by simp [h]\\n _ = b := by\\n exact (sub_add_cancel b c)\",\n \"n_chars\": 172,\n \"n_subproofs\": 0,\n \"n_tactics\": 8,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"sub_add_cancel","text":"theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\n","fan_in":4,"n_lines":4,"n_chars":98,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"sub_add_cancel\",\n \"text\": \"theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\\n sub_add_cancel_of_lt a.isLt b.isLt\\n\\n\",\n \"fan_in\": 4,\n \"n_lines\": 4,\n \"n_chars\": 98,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"add_right_cancel","fan_in":0,"n_deps_direct":1,"n_deps_transitive":7,"n_lines":10,"n_chars":247,"n_subproofs":0,"n_tactics":8,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"add_right_cancel\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 7,\n \"n_lines\": 10,\n \"n_chars\": 247,\n \"n_subproofs\": 0,\n \"n_tactics\": 8,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · sorry\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := sorry\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := sorry\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := sorry\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\ntheorem add_right_cancel {a b c : Uint256} (h : a + c = b + c) : a = b := sorry\n\nend Uint256\n\nend Verity.Core\n"},"solution_file_content":{"kind":"string","value":"/-\n Core Uint256 Operations\n\n This module provides arithmetic operations with EVM semantics:\n - All operations wrap at 2^256 (modular arithmetic)\n - Division and modulo by zero return 0 (matches EVM)\n - Provides overflow/underflow detection predicates\n\n These operations ensure semantic equivalence between EDSL\n verification and compiled EVM execution.\n-/\n\nnamespace Verity.Core\n\n-- EVM maximum value for uint256\ndef MAX_UINT256 : Nat := 2^256 - 1\n\n-- 256-bit modulus\ndef UINT256_MODULUS : Nat := 2^256\n\nstructure Uint256 where\n val : Nat\n isLt : val < UINT256_MODULUS\n deriving DecidableEq\n\nnamespace Uint256\n\ndef modulus : Nat := UINT256_MODULUS\n\ntheorem modulus_pos : 0 < modulus := by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have h : 0 < (2 : Nat) ^ 256 := Nat.pow_pos h2\n simp [modulus]\n exact h\n\ndef ofNat (n : Nat) : Uint256 :=\n ⟨n % modulus, Nat.mod_lt _ modulus_pos⟩\n\ninstance : OfNat Uint256 n := ⟨ofNat n⟩\ninstance : Inhabited Uint256 := ⟨ofNat 0⟩\ninstance : Repr Uint256 := ⟨fun u _ => repr u.val⟩\ninstance : Coe Uint256 Nat := ⟨Uint256.val⟩\ninstance : Coe Nat Uint256 := ⟨ofNat⟩\ninstance : BEq Uint256 := ⟨fun a b => decide (a = b)⟩\n\ninstance : LawfulBEq Uint256 where\n eq_of_beq {a b} h := by\n simp only [BEq.beq] at h\n exact of_decide_eq_true h\n rfl {a} := by\n show decide (a = a) = true\n exact decide_eq_true rfl\n\n@[simp] theorem val_ofNat (n : Nat) : (ofNat n).val = n % modulus := rfl\n@[simp] theorem coe_ofNat (n : Nat) : ((ofNat n : Uint256) : Nat) = n % modulus := rfl\n\n@[simp] theorem val_zero : (0 : Uint256).val = 0 := by\n change (ofNat 0).val = 0\n simp [ofNat]\n\n@[simp] theorem ofNat_zero : ofNat 0 = (0 : Uint256) := rfl\n\n@[simp] theorem ofNat_one : ofNat 1 = (1 : Uint256) := rfl\n\n@[simp] theorem val_one : (1 : Uint256).val = 1 := by\n change (ofNat 1).val = 1\n have hlt : (1 : Nat) < modulus := by\n dsimp [modulus, UINT256_MODULUS]\n decide\n simp [ofNat, Nat.mod_eq_of_lt hlt]\n@[simp] theorem val_ite {c : Prop} [Decidable c] (t e : Uint256) :\n (ite c t e).val = ite c t.val e.val := by\n by_cases c <;> simp [*]\n\n-- Order instances\ninstance : LT Uint256 := ⟨fun a b => a.val < b.val⟩\ninstance : LE Uint256 := ⟨fun a b => a.val ≤ b.val⟩\ninstance (a b : Uint256) : Decidable (a < b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a < b)\n exact inferInstance\ninstance (a b : Uint256) : Decidable (a ≤ b) := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n change Decidable (a ≤ b)\n exact inferInstance\n\n@[simp] theorem le_def (a b : Uint256) : (a ≤ b) = (a.val ≤ b.val) := rfl\n@[simp] theorem lt_def (a b : Uint256) : (a < b) = (a.val < b.val) := rfl\n\n-- Modular addition (wraps at 2^256)\ndef add (a b : Uint256) : Uint256 := ofNat (a.val + b.val)\n\n-- Modular subtraction (two's complement wrapping)\ndef sub (a b : Uint256) : Uint256 :=\n if b.val ≤ a.val then\n ofNat (a.val - b.val)\n else\n ofNat (modulus - (b.val - a.val))\n\n-- Modular multiplication (wraps at 2^256)\ndef mul (a b : Uint256) : Uint256 := ofNat (a.val * b.val)\n\n/-- EVM EXP semantics: exponentiation modulo `2^256`. -/\ndef pow (base exponent : Uint256) : Uint256 := ofNat (base.val ^ exponent.val)\n\n-- Division (returns 0 on division by zero, matching EVM)\ndef div (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val / b.val)\n\n-- Modulo (returns 0 on mod by zero, matching EVM)\ndef mod (a b : Uint256) : Uint256 :=\n if b.val = 0 then ofNat 0 else ofNat (a.val % b.val)\n\n-- Bitwise operations (EVM semantics)\ndef and (a b : Uint256) : Uint256 := ofNat (Nat.land a.val b.val)\ndef or (a b : Uint256) : Uint256 := ofNat (Nat.lor a.val b.val)\ndef xor (a b : Uint256) : Uint256 := ofNat (Nat.xor a.val b.val)\ndef not (a : Uint256) : Uint256 := ofNat (MAX_UINT256 - a.val)\n\n-- Shifts (EVM semantics: shl(shift, value) computes value << shift)\n-- To match EVM convention, we put shift first\ndef shl (shift value : Uint256) : Uint256 := ofNat (value.val <<< shift.val)\ndef shr (shift value : Uint256) : Uint256 := ofNat (value.val >>> shift.val)\n\n-- EVM BYTE(i, x): extract byte i from x, where byte 0 is most significant.\ndef byte (index value : Uint256) : Uint256 :=\n if index.val > 31 then\n ofNat 0\n else\n ofNat ((value.val >>> ((31 - index.val) * 8)) &&& 0xff)\n\n-- EVM SIGNEXTEND(b, x): extend sign bit at byte position b\ndef signextend (byteIdx value : Uint256) : Uint256 :=\n let b := byteIdx.val\n if b ≥ 31 then value\n else\n let bitPos := b * 8 + 7\n let mask := 2 ^ (bitPos + 1) - 1\n if value.val &&& (2 ^ bitPos) ≠ 0 then\n ofNat (value.val ||| (modulus - 1 - mask))\n else\n ofNat (value.val &&& mask)\n\n-- Overflow detection predicates for safety proofs (on raw Nat values)\ndef willAddOverflow (a b : Uint256) : Bool :=\n a.val + b.val ≥ modulus\n\ndef willSubUnderflow (a b : Uint256) : Bool :=\n b.val > a.val\n\ndef willMulOverflow (a b : Uint256) : Bool :=\n a.val * b.val ≥ modulus\n\n-- Instances for infix operators\ninstance : HAdd Uint256 Uint256 Uint256 := ⟨add⟩\ninstance : HSub Uint256 Uint256 Uint256 := ⟨sub⟩\ninstance : HMul Uint256 Uint256 Uint256 := ⟨mul⟩\ninstance : HPow Uint256 Uint256 Uint256 := ⟨pow⟩\ninstance : HDiv Uint256 Uint256 Uint256 := ⟨div⟩\ninstance : HMod Uint256 Uint256 Uint256 := ⟨mod⟩\ninstance : Add Uint256 := ⟨add⟩\ninstance : Sub Uint256 := ⟨sub⟩\ninstance : Mul Uint256 := ⟨mul⟩\ninstance : Pow Uint256 Uint256 := ⟨pow⟩\ninstance : Div Uint256 := ⟨div⟩\ninstance : Mod Uint256 := ⟨mod⟩\n\n-- Lemmas for modular arithmetic reasoning when no overflow/underflow occurs.\n\ntheorem sub_val_of_gt {a b : Uint256} (h : b.val > a.val) :\n (sub a b).val = (modulus - (b.val - a.val)) % modulus := by\n have h' : ¬ b.val ≤ a.val := Nat.not_le_of_gt h\n simp [sub, h', ofNat]\n\n@[ext] theorem ext {a b : Uint256} (h : a.val = b.val) : a = b := by\n cases a with\n | mk a ha =>\n cases b with\n | mk b hb =>\n cases h\n have : ha = hb := by\n apply Subsingleton.elim\n cases this\n rfl\n\n@[simp] theorem ofNat_add (a b : Nat) : ofNat (a + b) = (ofNat a) + (ofNat b) := by\n apply ext\n simp [HAdd.hAdd, add, ofNat]\n exact Nat.add_mod a b modulus\n\n@[simp] theorem zero_add (a : Uint256) : (0 : Uint256) + a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 0 + a.val < modulus := by\n simp [Nat.zero_add]\n exact hlt\n calc\n ((0 : Uint256) + a).val = (0 + a.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = 0 + a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_zero (a : Uint256) : a + (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val + 0 < modulus := by\n simp [Nat.add_zero]\n exact hlt\n calc\n (a + (0 : Uint256)).val = (a.val + 0) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = a.val + 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem add_comm (a b : Uint256) : a + b = b + a := by\n apply ext\n calc\n (a + b).val = (a.val + b.val) % modulus := by\n simp [HAdd.hAdd, add, ofNat]\n _ = (b.val + a.val) % modulus := by\n simp [Nat.add_comm]\n _ = (b + a).val := by\n simp [HAdd.hAdd, add, ofNat]\n\n@[simp] theorem add_assoc (a b c : Uint256) : (a + b) + c = a + (b + c) := by\n apply ext\n let m : Nat := modulus\n have hmod_c : c.val % m = c.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact c.isLt)\n have hmod_a : a.val % m = a.val := Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n calc\n ((a + b) + c).val\n = (((a.val + b.val) % m) + c.val) % m := by\n simp [HAdd.hAdd, add, ofNat, m]\n _ = ((a.val + b.val) + c.val) % m := by\n -- Normalize through add_mod\n simp [Nat.add_mod, hmod_c]\n _ = (a.val + b.val + c.val) % m := by\n simp [Nat.add_assoc]\n _ = (a.val + (b.val + c.val)) % m := by\n simp [Nat.add_assoc]\n _ = ((a.val % m) + ((b.val + c.val) % m)) % m := by\n -- Reverse add_mod\n exact (Nat.add_mod a.val (b.val + c.val) m)\n _ = (a.val + ((b.val + c.val) % m)) % m := by\n simp [hmod_a]\n _ = (a + (b + c)).val := by\n simp [HAdd.hAdd, add, ofNat, m]\n\n@[simp] theorem add_left_comm (a b c : Uint256) : a + b + c = b + a + c := by\n calc\n a + b + c = (a + b) + c := rfl\n _ = (b + a) + c := by simp [add_comm]\n _ = b + a + c := rfl\n\n@[simp] theorem sub_zero (a : Uint256) : a - (0 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val - 0 < modulus := by\n simp [Nat.sub_zero]\n exact hlt\n calc\n (a - (0 : Uint256)).val = (a.val - 0) % modulus := by\n simp [HSub.hSub, sub]\n _ = a.val - 0 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem sub_self (a : Uint256) : a - a = 0 := by\n apply ext\n calc\n (a - a).val = (a.val - a.val) % modulus := by\n simp [HSub.hSub, sub]\n _ = 0 := by simp\n\n@[simp] theorem zero_mul (a : Uint256) : (0 : Uint256) * a = 0 := by\n apply ext\n calc\n ((0 : Uint256) * a).val = (0 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem mul_zero (a : Uint256) : a * (0 : Uint256) = 0 := by\n apply ext\n calc\n (a * (0 : Uint256)).val = (a.val * 0) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 0 := by simp\n\n@[simp] theorem one_mul (a : Uint256) : (1 : Uint256) * a = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : 1 * a.val < modulus := by\n simp [Nat.one_mul]\n exact hlt\n calc\n ((1 : Uint256) * a).val = (1 * a.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = 1 * a.val := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_one (a : Uint256) : a * (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val * 1 < modulus := by\n simp [Nat.mul_one]\n exact hlt\n calc\n (a * (1 : Uint256)).val = (a.val * 1) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = a.val * 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem mul_comm (a b : Uint256) : a * b = b * a := by\n apply ext\n calc\n (a * b).val = (a.val * b.val) % modulus := by\n simp [HMul.hMul, mul, ofNat]\n _ = (b.val * a.val) % modulus := by\n simp [Nat.mul_comm]\n _ = (b * a).val := by\n simp [HMul.hMul, mul, ofNat]\n\n@[simp] theorem add_mul (a b c : Uint256) : (a + b) * c = a * c + b * c := by\n apply ext\n let m : Nat := modulus\n calc\n ((a + b) * c).val\n = (((a.val + b.val) % m) * c.val) % m := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n _ = ((a.val + b.val) * c.val) % m := by\n -- drop the inner mod on the left factor\n simp [m]\n _ = (a.val * c.val + b.val * c.val) % m := by\n simp [Nat.add_mul]\n _ = (((a.val * c.val) % m) + ((b.val * c.val) % m)) % m := by\n -- expand with add_mod\n exact (Nat.add_mod (a.val * c.val) (b.val * c.val) m)\n _ = (a * c + b * c).val := by\n simp [HMul.hMul, HAdd.hAdd, add, mul, ofNat, m]\n\n@[simp] theorem sub_add_cancel_left (a b : Uint256) : (a - b) + b = a := by\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n · have hlt : a.val - b.val < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n calc\n ((a - b) + b).val\n = (((a.val - b.val) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n _ = ((a.val - b.val) + b.val) % m := by\n simp [Nat.mod_eq_of_lt hlt]\n _ = a.val % m := by\n simp [Nat.sub_add_cancel h]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n have hsum : m - d + b.val = m + a.val := by\n -- b = a + (b - a)\n have hba_eq : b.val = a.val + d := by\n have h' : b.val = d + a.val := by\n symm\n exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n calc\n b.val = d + a.val := h'\n _ = a.val + d := by simp [Nat.add_comm]\n calc\n m - d + b.val\n = m - d + (a.val + d) := by simp [hba_eq]\n _ = (m - d + d) + a.val := by\n simp [Nat.add_assoc, Nat.add_comm]\n _ = m + a.val := by\n have hle : d ≤ m := Nat.le_of_lt hba\n simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n simp [HAdd.hAdd, HSub.hSub, sub, add, ofNat, m, h, d]\n _ = ((m - d) + b.val) % m := by\n simp\n _ = (m + a.val) % m := by\n simp [hsum]\n _ = a.val % m := by\n simp [Nat.add_mod_left]\n _ = a.val := by\n exact Nat.mod_eq_of_lt (by\n simp [m]\n exact a.isLt)\n\n@[simp] theorem div_one (a : Uint256) : a / (1 : Uint256) = a := by\n apply ext\n have hlt : a.val < modulus := a.isLt\n have hlt' : a.val / 1 < modulus := by\n simp [Nat.div_one]\n exact hlt\n calc\n (a / (1 : Uint256)).val = (a.val / 1) % modulus := by\n simp [HDiv.hDiv, div, ofNat]\n _ = a.val / 1 := by\n exact Nat.mod_eq_of_lt hlt'\n _ = a.val := by simp\n\n@[simp] theorem zero_div (a : Uint256) : (0 : Uint256) / a = 0 := by\n apply ext\n by_cases h : a.val = 0\n · simp [HDiv.hDiv, div, h]\n · calc\n ((0 : Uint256) / a).val = (0 / a.val) % modulus := by\n simp [HDiv.hDiv, div, h, ofNat]\n _ = 0 := by simp\n\ntheorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by\n simp [m]\n exact ha\n have hb'' : b < m := by\n simp [m]\n exact hb\n by_cases h : a + b < m\n · have hb_le : b ≤ a + b := Nat.le_add_left _ _\n have hmod : (a + b) % m = a + b := Nat.mod_eq_of_lt h\n have hb_le' : b ≤ (a + b) % m := by\n calc b\n _ ≤ a + b := hb_le\n _ = (a + b) % m := hmod.symm\n have hb_le_modulus : b ≤ (a + b) % modulus := by\n simpa [m] using hb_le'\n -- No overflow: direct cancellation.\n calc\n (sub (add ⟨a, ha'⟩ ⟨b, hb'⟩) ⟨b, hb'⟩).val = ((a + b) % m - b) % m := by\n simp [add, sub, ofNat, hb_le_modulus, m]\n _ = ((a + b) % m - b) % m := rfl\n _ = (a + b - b) % m := by rw [hmod]\n _ = a % m := by rw [Nat.add_sub_cancel]\n _ = a := Nat.mod_eq_of_lt ha''\n · have h_ge : m ≤ a + b := Nat.le_of_not_gt h\n have hlt_sum : a + b < m + m := Nat.add_lt_add ha'' hb''\n have hlt : a + b - m < m := Nat.sub_lt_left_of_lt_add h_ge hlt_sum\n have hmod : (a + b) % m = a + b - m := by\n have hmod' : (a + b) % m = (a + b - m) % m := Nat.mod_eq_sub_mod h_ge\n have hmod'' : (a + b - m) % m = a + b - m := Nat.mod_eq_of_lt hlt\n simp [hmod', hmod'']\n have hlt' : a + b < b + m := by\n have h' : a + b < m + b := Nat.add_lt_add_right ha'' b\n calc\n a + b < m + b := h'\n _ = b + m := by\n simp [Nat.add_comm]\n have hbgt : b > a + b - m := by\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n have hsum : (m - a) + (a + b - m) = b := by\n have hma : a ≤ m := Nat.le_of_lt ha''\n calc\n (m - a) + (a + b - m)\n = (m - a) + (a + b) - m := by\n symm\n exact Nat.add_sub_assoc h_ge (m - a)\n _ = ((m - a) + a) + b - m := by\n simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n _ = m + b - m := by\n simp [Nat.sub_add_cancel hma]\n _ = b := by\n exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n intro hc\n have : b ≤ a + b - m := by calc b\n _ ≤ (a + b) % m := hc\n _ = a + b - m := hmod\n exact hbnot this\n -- Overflow: wrap-around branch.\n let aU : Uint256 := ⟨a, ha'⟩\n let bU : Uint256 := ⟨b, hb'⟩\n have hma : a ≤ m := Nat.le_of_lt ha''\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n simp [Nat.add_comm])\n have hval' : (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := by\n have hgt : b > (a + b) % m := by\n exact Nat.lt_of_not_ge hbnot'\n have hgt' : bU.val > (add aU bU).val := by\n simp [aU, bU, add, ofNat]\n exact hgt\n calc\n (aU + bU - bU).val = (sub (add aU bU) bU).val := rfl\n _ = (m - (bU.val - (add aU bU).val)) % m := by\n simp [sub_val_of_gt, hgt', m]\n _ = (m - (b - (a + b) % m)) % m := by\n simp [aU, bU, add, ofNat, m]\n calc\n (aU + bU - bU).val = (m - (b - (a + b) % m)) % m := hval'\n _ = (m - (b - (a + b - m))) % m := by\n simp [hmod]\n _ = (m - (m - a)) % m := by\n simp [hdiff]\n _ = a % m := by\n simp [hsub]\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n\ntheorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\ntheorem add_right_cancel {a b c : Uint256} (h : a + c = b + c) : a = b := by\n calc\n a = a + c - c := by\n symm\n exact (sub_add_cancel a c)\n _ = b + c - c := by simp [h]\n _ = b := by\n exact (sub_add_cancel b c)\n\nend Uint256\n\nend Verity.Core\n"},"solution_diff":{"kind":"string","value":"@@ -356,12 +356,42 @@\n apply ext\n let m : Nat := modulus\n by_cases h : b.val ≤ a.val\n- · sorry\n+ · have hlt : a.val - b.val < m := by\n+ exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt\n+ have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt\n+ calc\n+ ((a - b) + b).val\n+ = (((a.val - b.val) % m) + b.val) % m := by\n+ simp [HAdd.hAdd, HSub.hSub, sub, h, add, ofNat, m]\n+ _ = ((a.val - b.val) + b.val) % m := by\n+ simp [Nat.mod_eq_of_lt hlt]\n+ _ = a.val % m := by\n+ simp [Nat.sub_add_cancel h]\n+ _ = a.val := by\n+ exact Nat.mod_eq_of_lt (by\n+ simp [m]\n+ exact a.isLt)\n · have hgt : b.val > a.val := Nat.lt_of_not_ge h\n let d : Nat := b.val - a.val\n have hba : d < m := by\n exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) b.isLt\n- have hsum : m - d + b.val = m + a.val := sorry\n+ have hsum : m - d + b.val = m + a.val := by\n+ -- b = a + (b - a)\n+ have hba_eq : b.val = a.val + d := by\n+ have h' : b.val = d + a.val := by\n+ symm\n+ exact Nat.sub_add_cancel (Nat.le_of_lt hgt)\n+ calc\n+ b.val = d + a.val := h'\n+ _ = a.val + d := by simp [Nat.add_comm]\n+ calc\n+ m - d + b.val\n+ = m - d + (a.val + d) := by simp [hba_eq]\n+ _ = (m - d + d) + a.val := by\n+ simp [Nat.add_assoc, Nat.add_comm]\n+ _ = m + a.val := by\n+ have hle : d ≤ m := Nat.le_of_lt hba\n+ simp [Nat.sub_add_cancel hle]\n calc\n ((a - b) + b).val\n = (((m - d) % m) + b.val) % m := by\n@@ -447,7 +477,19 @@\n exact Nat.sub_lt_right_of_lt_add h_ge hlt'\n have hbnot : ¬ b ≤ a + b - m := Nat.not_le_of_gt hbgt\n have hle : a + b - m ≤ b := Nat.le_of_lt hbgt\n- have hsum : (m - a) + (a + b - m) = b := sorry\n+ have hsum : (m - a) + (a + b - m) = b := by\n+ have hma : a ≤ m := Nat.le_of_lt ha''\n+ calc\n+ (m - a) + (a + b - m)\n+ = (m - a) + (a + b) - m := by\n+ symm\n+ exact Nat.add_sub_assoc h_ge (m - a)\n+ _ = ((m - a) + a) + b - m := by\n+ simp [Nat.add_assoc, Nat.add_left_comm, Nat.add_comm]\n+ _ = m + b - m := by\n+ simp [Nat.sub_add_cancel hma]\n+ _ = b := by\n+ exact Nat.add_sub_cancel_left m b\n have hdiff : b - (a + b - m) = m - a := by\n exact (Nat.sub_eq_iff_eq_add hle).2 hsum.symm\n have hbnot' : ¬ b ≤ (a + b) % m := by\n@@ -463,7 +505,7 @@\n have hsub : m - (m - a) = a := by\n have hle' : m - a ≤ m := Nat.sub_le _ _\n exact (Nat.sub_eq_iff_eq_add hle').2 (by\n- have h1 : m - a + a = m := sorry\n+ have h1 : m - a + a = m := Nat.sub_add_cancel hma\n calc\n m = m - a + a := h1.symm\n _ = a + (m - a) := by\n@@ -491,8 +533,18 @@\n _ = a := by\n exact Nat.mod_eq_of_lt ha''\n \n-theorem add_right_cancel {a b c : Uint256} (h : a + c = b + c) : a = b := sorry\n+theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n+ sub_add_cancel_of_lt a.isLt b.isLt\n \n+theorem add_right_cancel {a b c : Uint256} (h : a + c = b + c) : a = b := by\n+ calc\n+ a = a + c - c := by\n+ symm\n+ exact (sub_add_cancel a c)\n+ _ = b + c - c := by simp [h]\n+ _ = b := by\n+ exact (sub_add_cancel b c)\n+\n end Uint256\n \n end Verity.Core\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21353,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_0"},"challenge_id":{"kind":"string","value":"bde1c737ba5df7c6"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign","depth":1,"n_commands":0,"n_lines":19,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n refine { compileOk := hcompile, preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape_with_internals hcompile\n have hArgEq : argExprs' = argExprs := by simpa [hargCompile] using hargOk.symm\n subst hArgEq\n set singletonIR := [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢; rw [hlenOne] at hslack; rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩","n_chars":1133,"n_subproofs":8,"n_tactics":24,"cyclomatic":1,"n_automation":8,"n_rewrites":7,"n_structural":4,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 19,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n refine { compileOk := hcompile, preserves := ?_ }\\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape_with_internals hcompile\\n have hArgEq : argExprs' = argExprs := by simpa [hargCompile] using hargOk.symm\\n subst hArgEq\\n set singletonIR := [YulStmt.letMany names\\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\\n have hshape' : compiledIR = singletonIR := by simpa [singletonIR] using hshape\\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\\n have hExtraPos : 1 ≤ extraFuel := by\\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\\n set irFuel := extraFuel - 1 with hirFuel\\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\\n rw [hlenOne, hirFuel]; omega\\n rw [hshape'] at hslack ⊢; rw [hlenOne] at hslack; rw [hFuelEq]\\n exact ⟨_, _, rfl, rfl, hMatch⟩\",\n \"n_chars\": 1133,\n \"n_subproofs\": 8,\n \"n_tactics\": 24,\n \"cyclomatic\": 1,\n \"n_automation\": 8,\n \"n_rewrites\": 7,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compileStmt_internalCallAssign_shape_with_internals","text":"theorem compileStmt_internalCallAssign_shape_with_internals\n {fields : List CompilationModel.Field}\n {events : List EventDef}\n {errors : List ErrorDef}\n {scope : List String}\n {internalFunctions : List FunctionSpec}\n {names : List String}\n {functionName : String}\n {args : List CompilationModel.Expr}\n {compiledIR : List YulStmt}\n (hok :\n CompilationModel.compileStmt fields events errors .calldata [] false scope []\n (CompilationModel.Stmt.internalCallAssign names functionName args) internalFunctions =\n Except.ok compiledIR) :\n ∃ argExprs,\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n functionName args = Except.ok argExprs ∧\n compiledIR = [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName functionName) argExprs)] := by\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n bind, Except.bind] at hok\n match hargs :\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n functionName args with\n | .error e =>\n simp [hargs] at hok\n | .ok argExprs =>\n refine ⟨argExprs, rfl, ?_⟩\n simp [hargs, pure, Except.pure] at hok\n exact hok.symm\n\n","fan_in":1,"n_lines":32,"n_chars":1277,"n_subproofs":0,"n_tactics":12,"cyclomatic":2,"n_automation":4,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"compileStmt_internalCallAssign_shape_with_internals\",\n \"text\": \"theorem compileStmt_internalCallAssign_shape_with_internals\\n {fields : List CompilationModel.Field}\\n {events : List EventDef}\\n {errors : List ErrorDef}\\n {scope : List String}\\n {internalFunctions : List FunctionSpec}\\n {names : List String}\\n {functionName : String}\\n {args : List CompilationModel.Expr}\\n {compiledIR : List YulStmt}\\n (hok :\\n CompilationModel.compileStmt fields events errors .calldata [] false scope []\\n (CompilationModel.Stmt.internalCallAssign names functionName args) internalFunctions =\\n Except.ok compiledIR) :\\n ∃ argExprs,\\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\\n functionName args = Except.ok argExprs ∧\\n compiledIR = [YulStmt.letMany names\\n (YulExpr.call (CompilationModel.internalFunctionYulName functionName) argExprs)] := by\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\\n bind, Except.bind] at hok\\n match hargs :\\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\\n functionName args with\\n | .error e =>\\n simp [hargs] at hok\\n | .ok argExprs =>\\n refine ⟨argExprs, rfl, ?_⟩\\n simp [hargs, pure, Except.pure] at hok\\n exact hok.symm\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 32,\n \"n_chars\": 1277,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 4,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":49,"n_chars":2982,"n_subproofs":8,"n_tactics":24,"cyclomatic":1,"n_automation":8,"n_rewrites":7,"n_structural":4,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 49,\n \"n_chars\": 2982,\n \"n_subproofs\": 8,\n \"n_tactics\": 24,\n \"cyclomatic\": 1,\n \"n_automation\": 8,\n \"n_rewrites\": 7,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Spec-functions-aware constructor for the helper-aware single-step interface\nwhen the head statement is `Stmt.internalCallAssign`. -/\ntheorem compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign\n {runtimeContract : IRContract} {spec : CompilationModel} {fields : List Field}\n {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr}\n (hcompile :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR)\n (hargCompile :\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs)\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState) (state : IRState)\n (helperFuel irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n runtimeContract spec fields scope (Stmt.internalCallAssign names calleeName args) compiledIR := sorry\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\ntheorem compileStmt_internalCallAssign_shape_with_internals\n {fields : List CompilationModel.Field}\n {events : List EventDef}\n {errors : List ErrorDef}\n {scope : List String}\n {internalFunctions : List FunctionSpec}\n {names : List String}\n {functionName : String}\n {args : List CompilationModel.Expr}\n {compiledIR : List YulStmt}\n (hok :\n CompilationModel.compileStmt fields events errors .calldata [] false scope []\n (CompilationModel.Stmt.internalCallAssign names functionName args) internalFunctions =\n Except.ok compiledIR) :\n ∃ argExprs,\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n functionName args = Except.ok argExprs ∧\n compiledIR = [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName functionName) argExprs)] := by\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n bind, Except.bind] at hok\n match hargs :\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n functionName args with\n | .error e =>\n simp [hargs] at hok\n | .ok argExprs =>\n refine ⟨argExprs, rfl, ?_⟩\n simp [hargs, pure, Except.pure] at hok\n exact hok.symm\n\n/-- Spec-functions-aware constructor for the helper-aware single-step interface\nwhen the head statement is `Stmt.internalCallAssign`. -/\ntheorem compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign\n {runtimeContract : IRContract} {spec : CompilationModel} {fields : List Field}\n {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr}\n (hcompile :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR)\n (hargCompile :\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs)\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState) (state : IRState)\n (helperFuel irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n runtimeContract spec fields scope (Stmt.internalCallAssign names calleeName args) compiledIR := by\n refine { compileOk := hcompile, preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape_with_internals hcompile\n have hArgEq : argExprs' = argExprs := by simpa [hargCompile] using hargOk.symm\n subst hArgEq\n set singletonIR := [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢; rw [hlenOne] at hslack; rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -10,6 +10,37 @@\n open Compiler.CompilationModel\n open Compiler.Yul\n \n+theorem compileStmt_internalCallAssign_shape_with_internals\n+ {fields : List CompilationModel.Field}\n+ {events : List EventDef}\n+ {errors : List ErrorDef}\n+ {scope : List String}\n+ {internalFunctions : List FunctionSpec}\n+ {names : List String}\n+ {functionName : String}\n+ {args : List CompilationModel.Expr}\n+ {compiledIR : List YulStmt}\n+ (hok :\n+ CompilationModel.compileStmt fields events errors .calldata [] false scope []\n+ (CompilationModel.Stmt.internalCallAssign names functionName args) internalFunctions =\n+ Except.ok compiledIR) :\n+ ∃ argExprs,\n+ CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n+ functionName args = Except.ok argExprs ∧\n+ compiledIR = [YulStmt.letMany names\n+ (YulExpr.call (CompilationModel.internalFunctionYulName functionName) argExprs)] := by\n+ simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n+ bind, Except.bind] at hok\n+ match hargs :\n+ CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n+ functionName args with\n+ | .error e =>\n+ simp [hargs] at hok\n+ | .ok argExprs =>\n+ refine ⟨argExprs, rfl, ?_⟩\n+ simp [hargs, pure, Except.pure] at hok\n+ exact hok.symm\n+\n /-- Spec-functions-aware constructor for the helper-aware single-step interface\n when the head statement is `Stmt.internalCallAssign`. -/\n theorem compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign\n@@ -38,7 +69,25 @@\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n- runtimeContract spec fields scope (Stmt.internalCallAssign names calleeName args) compiledIR := sorry\n+ runtimeContract spec fields scope (Stmt.internalCallAssign names calleeName args) compiledIR := by\n+ refine { compileOk := hcompile, preserves := ?_ }\n+ intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n+ obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape_with_internals hcompile\n+ have hArgEq : argExprs' = argExprs := by simpa [hargCompile] using hargOk.symm\n+ subst hArgEq\n+ set singletonIR := [YulStmt.letMany names\n+ (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n+ have hshape' : compiledIR = singletonIR := by simpa [singletonIR] using hshape\n+ have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n+ have hExtraPos : 1 ≤ extraFuel := by\n+ have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n+ rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n+ set irFuel := extraFuel - 1 with hirFuel\n+ have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n+ have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n+ rw [hlenOne, hirFuel]; omega\n+ rw [hshape'] at hslack ⊢; rw [hlenOne] at hslack; rw [hFuelEq]\n+ exact ⟨_, _, rfl, rfl, hMatch⟩\n \n /-- Exact Tier 4 head-step proof object for a function body's direct internal\n helper surface. Future helper-rank induction should construct this single\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21354,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_1"},"challenge_id":{"kind":"string","value":"33a7fd2ac1c10484"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":1,"string":"1"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall","depth":1,"n_commands":0,"n_lines":19,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n refine { compileOk := hcompile, preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape_with_internals hcompile\n have hArgEq : argExprs' = argExprs := by simpa [hargCompile] using hargOk.symm\n subst hArgEq\n set singletonIR := [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢; rw [hlenOne] at hslack; rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩","n_chars":1122,"n_subproofs":8,"n_tactics":24,"cyclomatic":1,"n_automation":8,"n_rewrites":7,"n_structural":4,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 19,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n refine { compileOk := hcompile, preserves := ?_ }\\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape_with_internals hcompile\\n have hArgEq : argExprs' = argExprs := by simpa [hargCompile] using hargOk.symm\\n subst hArgEq\\n set singletonIR := [YulStmt.exprStmt\\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\\n have hshape' : compiledIR = singletonIR := by simpa [singletonIR] using hshape\\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\\n have hExtraPos : 1 ≤ extraFuel := by\\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\\n set irFuel := extraFuel - 1 with hirFuel\\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\\n rw [hlenOne, hirFuel]; omega\\n rw [hshape'] at hslack ⊢; rw [hlenOne] at hslack; rw [hFuelEq]\\n exact ⟨_, _, rfl, rfl, hMatch⟩\",\n \"n_chars\": 1122,\n \"n_subproofs\": 8,\n \"n_tactics\": 24,\n \"cyclomatic\": 1,\n \"n_automation\": 8,\n \"n_rewrites\": 7,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compileStmt_internalCall_shape_with_internals","text":"theorem compileStmt_internalCall_shape_with_internals\n {fields : List CompilationModel.Field}\n {events : List EventDef}\n {errors : List ErrorDef}\n {scope : List String}\n {internalFunctions : List FunctionSpec}\n {functionName : String}\n {args : List CompilationModel.Expr}\n {compiledIR : List YulStmt}\n (hok :\n CompilationModel.compileStmt fields events errors .calldata [] false scope []\n (CompilationModel.Stmt.internalCall functionName args) internalFunctions =\n Except.ok compiledIR) :\n ∃ argExprs,\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n functionName args = Except.ok argExprs ∧\n compiledIR = [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName functionName) argExprs)] := by\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n bind, Except.bind] at hok\n match hargs :\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n functionName args with\n | .error e =>\n simp [hargs] at hok\n | .ok argExprs =>\n refine ⟨argExprs, rfl, ?_⟩\n simp [hargs, pure, Except.pure] at hok\n exact hok.symm\n\n","fan_in":1,"n_lines":31,"n_chars":1228,"n_subproofs":0,"n_tactics":12,"cyclomatic":2,"n_automation":4,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"compileStmt_internalCall_shape_with_internals\",\n \"text\": \"theorem compileStmt_internalCall_shape_with_internals\\n {fields : List CompilationModel.Field}\\n {events : List EventDef}\\n {errors : List ErrorDef}\\n {scope : List String}\\n {internalFunctions : List FunctionSpec}\\n {functionName : String}\\n {args : List CompilationModel.Expr}\\n {compiledIR : List YulStmt}\\n (hok :\\n CompilationModel.compileStmt fields events errors .calldata [] false scope []\\n (CompilationModel.Stmt.internalCall functionName args) internalFunctions =\\n Except.ok compiledIR) :\\n ∃ argExprs,\\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\\n functionName args = Except.ok argExprs ∧\\n compiledIR = [YulStmt.exprStmt\\n (YulExpr.call (CompilationModel.internalFunctionYulName functionName) argExprs)] := by\\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\\n bind, Except.bind] at hok\\n match hargs :\\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\\n functionName args with\\n | .error e =>\\n simp [hargs] at hok\\n | .ok argExprs =>\\n refine ⟨argExprs, rfl, ?_⟩\\n simp [hargs, pure, Except.pure] at hok\\n exact hok.symm\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 31,\n \"n_chars\": 1228,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 4,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":49,"n_chars":2884,"n_subproofs":8,"n_tactics":24,"cyclomatic":1,"n_automation":8,"n_rewrites":7,"n_structural":4,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 49,\n \"n_chars\": 2884,\n \"n_subproofs\": 8,\n \"n_tactics\": 24,\n \"cyclomatic\": 1,\n \"n_automation\": 8,\n \"n_rewrites\": 7,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Spec-functions-aware constructor for the helper-aware single-step interface\nwhen the head statement is `Stmt.internalCall`. -/\ntheorem compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall\n {runtimeContract : IRContract} {spec : CompilationModel} {fields : List Field}\n {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr}\n (hcompile :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR)\n (hargCompile :\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs)\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState) (state : IRState)\n (helperFuel irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n runtimeContract spec fields scope (Stmt.internalCall calleeName args) compiledIR := sorry\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\ntheorem compileStmt_internalCall_shape_with_internals\n {fields : List CompilationModel.Field}\n {events : List EventDef}\n {errors : List ErrorDef}\n {scope : List String}\n {internalFunctions : List FunctionSpec}\n {functionName : String}\n {args : List CompilationModel.Expr}\n {compiledIR : List YulStmt}\n (hok :\n CompilationModel.compileStmt fields events errors .calldata [] false scope []\n (CompilationModel.Stmt.internalCall functionName args) internalFunctions =\n Except.ok compiledIR) :\n ∃ argExprs,\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n functionName args = Except.ok argExprs ∧\n compiledIR = [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName functionName) argExprs)] := by\n simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n bind, Except.bind] at hok\n match hargs :\n CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n functionName args with\n | .error e =>\n simp [hargs] at hok\n | .ok argExprs =>\n refine ⟨argExprs, rfl, ?_⟩\n simp [hargs, pure, Except.pure] at hok\n exact hok.symm\n\n/-- Spec-functions-aware constructor for the helper-aware single-step interface\nwhen the head statement is `Stmt.internalCall`. -/\ntheorem compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall\n {runtimeContract : IRContract} {spec : CompilationModel} {fields : List Field}\n {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr}\n (hcompile :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR)\n (hargCompile :\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs)\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState) (state : IRState)\n (helperFuel irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n runtimeContract spec fields scope (Stmt.internalCall calleeName args) compiledIR := by\n refine { compileOk := hcompile, preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape_with_internals hcompile\n have hArgEq : argExprs' = argExprs := by simpa [hargCompile] using hargOk.symm\n subst hArgEq\n set singletonIR := [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢; rw [hlenOne] at hslack; rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -10,6 +10,36 @@\n open Compiler.CompilationModel\n open Compiler.Yul\n \n+theorem compileStmt_internalCall_shape_with_internals\n+ {fields : List CompilationModel.Field}\n+ {events : List EventDef}\n+ {errors : List ErrorDef}\n+ {scope : List String}\n+ {internalFunctions : List FunctionSpec}\n+ {functionName : String}\n+ {args : List CompilationModel.Expr}\n+ {compiledIR : List YulStmt}\n+ (hok :\n+ CompilationModel.compileStmt fields events errors .calldata [] false scope []\n+ (CompilationModel.Stmt.internalCall functionName args) internalFunctions =\n+ Except.ok compiledIR) :\n+ ∃ argExprs,\n+ CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n+ functionName args = Except.ok argExprs ∧\n+ compiledIR = [YulStmt.exprStmt\n+ (YulExpr.call (CompilationModel.internalFunctionYulName functionName) argExprs)] := by\n+ simp only [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork,\n+ bind, Except.bind] at hok\n+ match hargs :\n+ CompilationModel.compileInternalCallArgs fields .calldata internalFunctions\n+ functionName args with\n+ | .error e =>\n+ simp [hargs] at hok\n+ | .ok argExprs =>\n+ refine ⟨argExprs, rfl, ?_⟩\n+ simp [hargs, pure, Except.pure] at hok\n+ exact hok.symm\n+\n /-- Spec-functions-aware constructor for the helper-aware single-step interface\n when the head statement is `Stmt.internalCall`. -/\n theorem compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall\n@@ -38,7 +68,25 @@\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n- runtimeContract spec fields scope (Stmt.internalCall calleeName args) compiledIR := sorry\n+ runtimeContract spec fields scope (Stmt.internalCall calleeName args) compiledIR := by\n+ refine { compileOk := hcompile, preserves := ?_ }\n+ intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n+ obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape_with_internals hcompile\n+ have hArgEq : argExprs' = argExprs := by simpa [hargCompile] using hargOk.symm\n+ subst hArgEq\n+ set singletonIR := [YulStmt.exprStmt\n+ (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n+ have hshape' : compiledIR = singletonIR := by simpa [singletonIR] using hshape\n+ have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n+ have hExtraPos : 1 ≤ extraFuel := by\n+ have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n+ rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n+ set irFuel := extraFuel - 1 with hirFuel\n+ have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n+ have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n+ rw [hlenOne, hirFuel]; omega\n+ rw [hshape'] at hslack ⊢; rw [hlenOne] at hslack; rw [hFuelEq]\n+ exact ⟨_, _, rfl, rfl, hMatch⟩\n \n /-- Exact Tier 4 head-step proof object for a function body's direct internal\n helper surface. Future helper-rank induction should construct this single\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21355,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_2"},"challenge_id":{"kind":"string","value":"ce4101ea17d25db3"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":2,"string":"2"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog","depth":1,"n_commands":0,"n_lines":14,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n exact\n directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n (directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n hbody\n hassign)","n_chars":425,"n_subproofs":0,"n_tactics":14,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 14,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n exact\\n directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\\n (runtimeContract := runtimeContract)\\n (spec := spec)\\n (fields := fields)\\n (fn := fn)\\n (directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\\n (runtimeContract := runtimeContract)\\n (spec := spec)\\n (fields := fields)\\n (fn := fn)\\n hbody\\n hassign)\",\n \"n_chars\": 425,\n \"n_subproofs\": 0,\n \"n_tactics\": 14,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog","text":"/-- Reassemble the full callee-local bridge catalog from the current supported\nbody witness plus the assign-only bridge half. The call half is vacuous because\n`SupportedStmtList` still excludes direct helper calls from the fragment. -/\ntheorem directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · intro calleeName hmem\n exfalso\n simp [hbody.helperCallNames_nil] at hmem\n · intro calleeName hmem\n exact hassign.assign hmem\n\n","fan_in":1,"n_lines":20,"n_chars":840,"n_subproofs":0,"n_tactics":7,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":4,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\",\n \"text\": \"/-- Reassemble the full callee-local bridge catalog from the current supported\\nbody witness plus the assign-only bridge half. The call half is vacuous because\\n`SupportedStmtList` still excludes direct helper calls from the fragment. -/\\ntheorem directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\\n {runtimeContract : IRContract}\\n {spec : CompilationModel}\\n {fields : List Field}\\n {fn : FunctionSpec}\\n (hbody : SupportedBodyInterface spec fn)\\n (hassign :\\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\\n DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn := by\\n refine ⟨?_, ?_⟩\\n · intro calleeName hmem\\n exfalso\\n simp [hbody.helperCallNames_nil] at hmem\\n · intro calleeName hmem\\n exact hassign.assign hmem\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 20,\n \"n_chars\": 840,\n \"n_subproofs\": 0,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog","fan_in":1,"n_deps_direct":2,"n_deps_transitive":2,"n_lines":28,"n_chars":1171,"n_subproofs":0,"n_tactics":14,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\",\n \"fan_in\": 1,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 2,\n \"n_lines\": 28,\n \"n_chars\": 1171,\n \"n_subproofs\": 0,\n \"n_tactics\": 14,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\ntheorem directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hcallee : DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro scope calleeName args hmem\n exact (hcallee.call hmem).compile (scope := scope) (args := args)\n · intro scope calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.call hmem).bridge\n (scope := scope)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n · intro scope names calleeName args hmem\n exact (hcallee.assign hmem).compile (scope := scope) (names := names) (args := args)\n · intro scope names calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.assign hmem).bridge\n (scope := scope)\n (names := names)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n\n/-- Assemble the body-level direct-helper bridge catalog directly from the\ncurrent helper-free supported-body witness plus the assign-only per-callee\nbridge inventory. This keeps downstream theorems on the exact assign-only Tier 4\nboundary instead of routing through the vacuous per-callee void-call layer. -/\ntheorem directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := sorry\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Reassemble the full callee-local bridge catalog from the current supported\nbody witness plus the assign-only bridge half. The call half is vacuous because\n`SupportedStmtList` still excludes direct helper calls from the fragment. -/\ntheorem directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · intro calleeName hmem\n exfalso\n simp [hbody.helperCallNames_nil] at hmem\n · intro calleeName hmem\n exact hassign.assign hmem\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\ntheorem directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hcallee : DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro scope calleeName args hmem\n exact (hcallee.call hmem).compile (scope := scope) (args := args)\n · intro scope calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.call hmem).bridge\n (scope := scope)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n · intro scope names calleeName args hmem\n exact (hcallee.assign hmem).compile (scope := scope) (names := names) (args := args)\n · intro scope names calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.assign hmem).bridge\n (scope := scope)\n (names := names)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n\n/-- Assemble the body-level direct-helper bridge catalog directly from the\ncurrent helper-free supported-body witness plus the assign-only per-callee\nbridge inventory. This keeps downstream theorems on the exact assign-only Tier 4\nboundary instead of routing through the vacuous per-callee void-call layer. -/\ntheorem directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n exact\n directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n (directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n hbody\n hassign)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -281,6 +281,25 @@\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n \n+/-- Reassemble the full callee-local bridge catalog from the current supported\n+body witness plus the assign-only bridge half. The call half is vacuous because\n+`SupportedStmtList` still excludes direct helper calls from the fragment. -/\n+theorem directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n+ {runtimeContract : IRContract}\n+ {spec : CompilationModel}\n+ {fields : List Field}\n+ {fn : FunctionSpec}\n+ (hbody : SupportedBodyInterface spec fn)\n+ (hassign :\n+ DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n+ DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn := by\n+ refine ⟨?_, ?_⟩\n+ · intro calleeName hmem\n+ exfalso\n+ simp [hbody.helperCallNames_nil] at hmem\n+ · intro calleeName hmem\n+ exact hassign.assign hmem\n+\n /-- Split compile-side Tier 4 inventory. This isolates the purely compilation\n obligations from the semantic bridge obligations so future fragment widening can\n discharge compile success generically once direct helper calls are admitted into\n@@ -354,7 +373,20 @@\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n- DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := sorry\n+ DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n+ exact\n+ directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n+ (runtimeContract := runtimeContract)\n+ (spec := spec)\n+ (fields := fields)\n+ (fn := fn)\n+ (directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n+ (runtimeContract := runtimeContract)\n+ (spec := spec)\n+ (fields := fields)\n+ (fn := fn)\n+ hbody\n+ hassign)\n \n end Compiler.Proofs.IRGeneration\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21356,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_3"},"challenge_id":{"kind":"string","value":"cb08e4831eecb217"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":3,"string":"3"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"directInternalHelperHeadStepCatalog_call_of_bridgeCatalog","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n (args := args) hmem with ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCall\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompileSpec\n hargCompile\n (hbridge.callBridge\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)","n_chars":1120,"n_subproofs":2,"n_tactics":31,"cyclomatic":2,"n_automation":1,"n_rewrites":0,"n_structural":5,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro scope calleeName args hmem\\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\\n (args := args) hmem with ⟨compiledIR, hcompile⟩\\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\\n Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n refine ⟨compiledIR, ?_⟩\\n exact\\n compiledStmtStepWithHelpersAndHelperIR_internalCall\\n (runtimeContract := runtimeContract)\\n (spec := spec)\\n (fields := fields)\\n (scope := scope)\\n (calleeName := calleeName)\\n (args := args)\\n (compiledIR := compiledIR)\\n (argExprs := argExprs)\\n hcompileSpec\\n hargCompile\\n (hbridge.callBridge\\n (scope := scope)\\n (calleeName := calleeName)\\n (args := args)\\n (compiledIR := compiledIR)\\n (argExprs := argExprs)\\n hmem\\n hcompile\\n hargCompile)\",\n \"n_chars\": 1120,\n \"n_subproofs\": 2,\n \"n_tactics\": 31,\n \"cyclomatic\": 2,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compiledStmtStepWithHelpersAndHelperIR_internalCall","text":"theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by\n simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack\n rw [hlenOne] at hslack\n omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n","fan_in":1,"n_lines":68,"n_chars":3140,"n_subproofs":9,"n_tactics":35,"cyclomatic":1,"n_automation":10,"n_rewrites":7,"n_structural":5,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStepWithHelpersAndHelperIR_internalCall\",\n \"text\": \"theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\\n {runtimeContract : IRContract}\\n {spec : CompilationModel}\\n {fields : List Field}\\n {scope : List String}\\n {calleeName : String} {args : List Expr}\\n {compiledIR : List YulStmt}\\n {argExprs : List YulExpr}\\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\\n -- End-to-end source↔IR alignment bridge.\\n (bridge :\\n ∀ (runtime : SourceSemantics.RuntimeState)\\n (state : IRState)\\n (helperFuel : Nat)\\n (irFuel : Nat),\\n 0 < helperFuel →\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\\n FunctionBody.scopeNamesPresent scope runtime.bindings →\\n FunctionBody.bindingsBounded runtime.bindings →\\n FunctionBody.runtimeStateMatchesIR fields runtime state →\\n stmtStepMatchesIRExecWithInternals fields\\n (stmtNextScope scope (Stmt.internalCall calleeName args))\\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\\n (Stmt.internalCall calleeName args))\\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\\n [YulStmt.exprStmt (YulExpr.call\\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\\n CompiledStmtStepWithHelpersAndHelperIR\\n runtimeContract spec fields scope\\n (Stmt.internalCall calleeName args)\\n compiledIR := by\\n refine {\\n compileOk := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n preserves := ?_ }\\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\\n have hArgEq : argExprs' = argExprs := by\\n simp [hargCompile] at hargOk\\n exact hargOk.symm\\n subst hArgEq\\n set singletonIR :=\\n [YulStmt.exprStmt\\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\\n have hshape' : compiledIR = singletonIR := by\\n simpa [singletonIR] using hshape\\n have hlenOne : singletonIR.length = 1 := by\\n simp [singletonIR]\\n have hExtraPos : 1 ≤ extraFuel := by\\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\\n rw [hshape'] at hslack\\n rw [hlenOne] at hslack\\n omega\\n set irFuel := extraFuel - 1 with hirFuel\\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\\n rw [hlenOne, hirFuel]; omega\\n rw [hshape'] at hslack ⊢\\n rw [hlenOne] at hslack\\n rw [hFuelEq]\\n exact ⟨_, _, rfl, rfl, hMatch⟩\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 68,\n \"n_chars\": 3140,\n \"n_subproofs\": 9,\n \"n_tactics\": 35,\n \"cyclomatic\": 1,\n \"n_automation\": 10,\n \"n_rewrites\": 7,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"directInternalHelperHeadStepCatalog_call_of_bridgeCatalog","fan_in":1,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":48,"n_chars":1730,"n_subproofs":2,"n_tactics":31,"cyclomatic":2,"n_automation":1,"n_rewrites":0,"n_structural":5,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\",\n \"fan_in\": 1,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 48,\n \"n_chars\": 1730,\n \"n_subproofs\": 2,\n \"n_tactics\": 31,\n \"cyclomatic\": 2,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR := sorry\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by\n simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack\n rw [hlenOne] at hslack\n omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n (args := args) hmem with ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCall\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompileSpec\n hargCompile\n (hbridge.callBridge\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -10,6 +10,73 @@\n open Compiler.CompilationModel\n open Compiler.Yul\n \n+theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n+ {runtimeContract : IRContract}\n+ {spec : CompilationModel}\n+ {fields : List Field}\n+ {scope : List String}\n+ {calleeName : String} {args : List Expr}\n+ {compiledIR : List YulStmt}\n+ {argExprs : List YulExpr}\n+ (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n+ (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n+ (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n+ -- End-to-end source↔IR alignment bridge.\n+ (bridge :\n+ ∀ (runtime : SourceSemantics.RuntimeState)\n+ (state : IRState)\n+ (helperFuel : Nat)\n+ (irFuel : Nat),\n+ 0 < helperFuel →\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n+ FunctionBody.scopeNamesPresent scope runtime.bindings →\n+ FunctionBody.bindingsBounded runtime.bindings →\n+ FunctionBody.runtimeStateMatchesIR fields runtime state →\n+ stmtStepMatchesIRExecWithInternals fields\n+ (stmtNextScope scope (Stmt.internalCall calleeName args))\n+ (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n+ (Stmt.internalCall calleeName args))\n+ (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n+ [YulStmt.exprStmt (YulExpr.call\n+ (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n+ CompiledStmtStepWithHelpersAndHelperIR\n+ runtimeContract spec fields scope\n+ (Stmt.internalCall calleeName args)\n+ compiledIR := by\n+ refine {\n+ compileOk := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ preserves := ?_ }\n+ intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n+ have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n+ (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n+ have hArgEq : argExprs' = argExprs := by\n+ simp [hargCompile] at hargOk\n+ exact hargOk.symm\n+ subst hArgEq\n+ set singletonIR :=\n+ [YulStmt.exprStmt\n+ (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n+ have hshape' : compiledIR = singletonIR := by\n+ simpa [singletonIR] using hshape\n+ have hlenOne : singletonIR.length = 1 := by\n+ simp [singletonIR]\n+ have hExtraPos : 1 ≤ extraFuel := by\n+ have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n+ rw [hshape'] at hslack\n+ rw [hlenOne] at hslack\n+ omega\n+ set irFuel := extraFuel - 1 with hirFuel\n+ have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n+ have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n+ rw [hlenOne, hirFuel]; omega\n+ rw [hshape'] at hslack ⊢\n+ rw [hlenOne] at hslack\n+ rw [hFuelEq]\n+ exact ⟨_, _, rfl, rfl, hMatch⟩\n+\n /-- Exact Tier 4 head-step proof object for a function body's direct internal\n helper surface. Future helper-rank induction should construct this single\n catalog once, then reuse the mechanical list-interface assembly theorems\n@@ -327,7 +394,37 @@\n fields\n scope\n (Stmt.internalCall calleeName args)\n- compiledIR := sorry\n+ compiledIR := by\n+ intro scope calleeName args hmem\n+ rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n+ (args := args) hmem with ⟨compiledIR, hcompile⟩\n+ obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n+ have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n+ .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n+ Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ refine ⟨compiledIR, ?_⟩\n+ exact\n+ compiledStmtStepWithHelpersAndHelperIR_internalCall\n+ (runtimeContract := runtimeContract)\n+ (spec := spec)\n+ (fields := fields)\n+ (scope := scope)\n+ (calleeName := calleeName)\n+ (args := args)\n+ (compiledIR := compiledIR)\n+ (argExprs := argExprs)\n+ hcompileSpec\n+ hargCompile\n+ (hbridge.callBridge\n+ (scope := scope)\n+ (calleeName := calleeName)\n+ (args := args)\n+ (compiledIR := compiledIR)\n+ (argExprs := argExprs)\n+ hmem\n+ hcompile\n+ hargCompile)\n \n end Compiler.Proofs.IRGeneration\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21357,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_4"},"challenge_id":{"kind":"string","value":"2d7fa8964b45955c"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":4,"string":"4"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog","depth":1,"n_commands":0,"n_lines":24,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n have hcompileSpec :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n hcompileSpec\n hargCompile\n (hbridge.assignBridge\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)","n_chars":966,"n_subproofs":2,"n_tactics":24,"cyclomatic":2,"n_automation":1,"n_rewrites":0,"n_structural":5,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 24,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro scope names calleeName args hmem\\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\\n ⟨compiledIR, hcompile⟩\\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\\n have hcompileSpec :\\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n refine ⟨compiledIR, ?_⟩\\n exact\\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\\n hcompileSpec\\n hargCompile\\n (hbridge.assignBridge\\n (scope := scope)\\n (names := names)\\n (calleeName := calleeName)\\n (args := args)\\n (compiledIR := compiledIR)\\n (argExprs := argExprs)\\n hmem\\n hcompile\\n hargCompile)\",\n \"n_chars\": 966,\n \"n_subproofs\": 2,\n \"n_tactics\": 24,\n \"cyclomatic\": 2,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compiledStmtStepWithHelpersAndHelperIR_internalCallAssign","text":"/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\nsupply. The bridge captures the end-to-end obligation: given matching\npreconditions, the source and IR execution results for this statement match\nthrough `stmtStepMatchesIRExecWithInternals`.\n\nThe bridge is quantified over an extra `irFuel` so that the proof can\ninstantiate it at the right fuel level derived from `extraFuel`.\n\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n","fan_in":1,"n_lines":76,"n_chars":3873,"n_subproofs":9,"n_tactics":34,"cyclomatic":1,"n_automation":10,"n_rewrites":7,"n_structural":5,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\",\n \"text\": \"/-- Constructor for the helper-aware single-step interface when the head\\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\\nsupply. The bridge captures the end-to-end obligation: given matching\\npreconditions, the source and IR execution results for this statement match\\nthrough `stmtStepMatchesIRExecWithInternals`.\\n\\nThe bridge is quantified over an extra `irFuel` so that the proof can\\ninstantiate it at the right fuel level derived from `extraFuel`.\\n\\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\\n {runtimeContract : IRContract}\\n {spec : CompilationModel}\\n {fields : List Field}\\n {scope : List String}\\n {names : List String} {calleeName : String} {args : List Expr}\\n {compiledIR : List YulStmt}\\n {argExprs : List YulExpr}\\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\\n -- End-to-end source↔IR alignment bridge.\\n (bridge :\\n ∀ (runtime : SourceSemantics.RuntimeState)\\n (state : IRState)\\n (helperFuel : Nat)\\n (irFuel : Nat),\\n 0 < helperFuel →\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\\n FunctionBody.scopeNamesPresent scope runtime.bindings →\\n FunctionBody.bindingsBounded runtime.bindings →\\n FunctionBody.runtimeStateMatchesIR fields runtime state →\\n stmtStepMatchesIRExecWithInternals fields\\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\\n (Stmt.internalCallAssign names calleeName args))\\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\\n [YulStmt.letMany names (YulExpr.call\\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\\n CompiledStmtStepWithHelpersAndHelperIR\\n runtimeContract spec fields scope\\n (Stmt.internalCallAssign names calleeName args)\\n compiledIR := by\\n refine {\\n compileOk := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n preserves := ?_ }\\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\\n have hArgEq : argExprs' = argExprs := by\\n simp [hargCompile] at hargOk\\n exact hargOk.symm\\n subst hArgEq\\n set singletonIR :=\\n [YulStmt.letMany names\\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\\n have hshape' : compiledIR = singletonIR := by\\n simpa [singletonIR] using hshape\\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\\n have hExtraPos : 1 ≤ extraFuel := by\\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\\n set irFuel := extraFuel - 1 with hirFuel\\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\\n rw [hlenOne, hirFuel]; omega\\n rw [hshape'] at hslack ⊢\\n rw [hlenOne] at hslack\\n rw [hFuelEq]\\n exact ⟨_, _, rfl, rfl, hMatch⟩\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 76,\n \"n_chars\": 3873,\n \"n_subproofs\": 9,\n \"n_tactics\": 34,\n \"cyclomatic\": 1,\n \"n_automation\": 10,\n \"n_rewrites\": 7,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog","fan_in":1,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":41,"n_chars":1612,"n_subproofs":2,"n_tactics":24,"cyclomatic":2,"n_automation":1,"n_rewrites":0,"n_structural":5,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\",\n \"fan_in\": 1,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 41,\n \"n_chars\": 1612,\n \"n_subproofs\": 2,\n \"n_tactics\": 24,\n \"cyclomatic\": 2,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := sorry\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\nsupply. The bridge captures the end-to-end obligation: given matching\npreconditions, the source and IR execution results for this statement match\nthrough `stmtStepMatchesIRExecWithInternals`.\n\nThe bridge is quantified over an extra `irFuel` so that the proof can\ninstantiate it at the right fuel level derived from `extraFuel`.\n\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n have hcompileSpec :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n hcompileSpec\n hargCompile\n (hbridge.assignBridge\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -10,6 +10,81 @@\n open Compiler.CompilationModel\n open Compiler.Yul\n \n+/-- Constructor for the helper-aware single-step interface when the head\n+statement is `Stmt.internalCallAssign`. The proof is parameterised by a single\n+source-to-IR alignment bridge that the rank-decreasing callee induction will\n+supply. The bridge captures the end-to-end obligation: given matching\n+preconditions, the source and IR execution results for this statement match\n+through `stmtStepMatchesIRExecWithInternals`.\n+\n+The bridge is quantified over an extra `irFuel` so that the proof can\n+instantiate it at the right fuel level derived from `extraFuel`.\n+\n+The `compileOk` obligation is passed through from the compilation hypothesis. -/\n+theorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n+ {runtimeContract : IRContract}\n+ {spec : CompilationModel}\n+ {fields : List Field}\n+ {scope : List String}\n+ {names : List String} {calleeName : String} {args : List Expr}\n+ {compiledIR : List YulStmt}\n+ {argExprs : List YulExpr}\n+ (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n+ (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n+ -- End-to-end source↔IR alignment bridge.\n+ (bridge :\n+ ∀ (runtime : SourceSemantics.RuntimeState)\n+ (state : IRState)\n+ (helperFuel : Nat)\n+ (irFuel : Nat),\n+ 0 < helperFuel →\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n+ FunctionBody.scopeNamesPresent scope runtime.bindings →\n+ FunctionBody.bindingsBounded runtime.bindings →\n+ FunctionBody.runtimeStateMatchesIR fields runtime state →\n+ stmtStepMatchesIRExecWithInternals fields\n+ (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n+ (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n+ (Stmt.internalCallAssign names calleeName args))\n+ (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n+ [YulStmt.letMany names (YulExpr.call\n+ (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n+ CompiledStmtStepWithHelpersAndHelperIR\n+ runtimeContract spec fields scope\n+ (Stmt.internalCallAssign names calleeName args)\n+ compiledIR := by\n+ refine {\n+ compileOk := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ preserves := ?_ }\n+ intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n+ have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n+ have hArgEq : argExprs' = argExprs := by\n+ simp [hargCompile] at hargOk\n+ exact hargOk.symm\n+ subst hArgEq\n+ set singletonIR :=\n+ [YulStmt.letMany names\n+ (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n+ have hshape' : compiledIR = singletonIR := by\n+ simpa [singletonIR] using hshape\n+ have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n+ have hExtraPos : 1 ≤ extraFuel := by\n+ have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n+ rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n+ set irFuel := extraFuel - 1 with hirFuel\n+ have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n+ have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n+ rw [hlenOne, hirFuel]; omega\n+ rw [hshape'] at hslack ⊢\n+ rw [hlenOne] at hslack\n+ rw [hFuelEq]\n+ exact ⟨_, _, rfl, rfl, hMatch⟩\n+\n /-- Exact Tier 4 head-step proof object for a function body's direct internal\n helper surface. Future helper-rank induction should construct this single\n catalog once, then reuse the mechanical list-interface assembly theorems\n@@ -327,7 +402,30 @@\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n- compiledIR := sorry\n+ compiledIR := by\n+ intro scope names calleeName args hmem\n+ rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n+ ⟨compiledIR, hcompile⟩\n+ obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n+ have hcompileSpec :\n+ CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ refine ⟨compiledIR, ?_⟩\n+ exact\n+ compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n+ hcompileSpec\n+ hargCompile\n+ (hbridge.assignBridge\n+ (scope := scope)\n+ (names := names)\n+ (calleeName := calleeName)\n+ (args := args)\n+ (compiledIR := compiledIR)\n+ (argExprs := argExprs)\n+ hmem\n+ hcompile\n+ hargCompile)\n \n end Compiler.Proofs.IRGeneration\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21358,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_5"},"challenge_id":{"kind":"string","value":"9d3735538da801c6"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":5,"string":"5"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog","depth":1,"n_commands":0,"n_lines":24,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n have hcompileSpec :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n hcompileSpec\n hargCompile\n (hbridge.assignBridge\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)","n_chars":966,"n_subproofs":2,"n_tactics":24,"cyclomatic":2,"n_automation":1,"n_rewrites":0,"n_structural":5,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 24,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro scope names calleeName args hmem\\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\\n ⟨compiledIR, hcompile⟩\\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\\n have hcompileSpec :\\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n refine ⟨compiledIR, ?_⟩\\n exact\\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\\n hcompileSpec\\n hargCompile\\n (hbridge.assignBridge\\n (scope := scope)\\n (names := names)\\n (calleeName := calleeName)\\n (args := args)\\n (compiledIR := compiledIR)\\n (argExprs := argExprs)\\n hmem\\n hcompile\\n hargCompile)\",\n \"n_chars\": 966,\n \"n_subproofs\": 2,\n \"n_tactics\": 24,\n \"cyclomatic\": 2,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compiledStmtStepWithHelpersAndHelperIR_internalCallAssign","text":"/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\nsupply. The bridge captures the end-to-end obligation: given matching\npreconditions, the source and IR execution results for this statement match\nthrough `stmtStepMatchesIRExecWithInternals`.\n\nThe bridge is quantified over an extra `irFuel` so that the proof can\ninstantiate it at the right fuel level derived from `extraFuel`.\n\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n","fan_in":1,"n_lines":76,"n_chars":3873,"n_subproofs":9,"n_tactics":34,"cyclomatic":1,"n_automation":10,"n_rewrites":7,"n_structural":5,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\",\n \"text\": \"/-- Constructor for the helper-aware single-step interface when the head\\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\\nsupply. The bridge captures the end-to-end obligation: given matching\\npreconditions, the source and IR execution results for this statement match\\nthrough `stmtStepMatchesIRExecWithInternals`.\\n\\nThe bridge is quantified over an extra `irFuel` so that the proof can\\ninstantiate it at the right fuel level derived from `extraFuel`.\\n\\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\\n {runtimeContract : IRContract}\\n {spec : CompilationModel}\\n {fields : List Field}\\n {scope : List String}\\n {names : List String} {calleeName : String} {args : List Expr}\\n {compiledIR : List YulStmt}\\n {argExprs : List YulExpr}\\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\\n -- End-to-end source↔IR alignment bridge.\\n (bridge :\\n ∀ (runtime : SourceSemantics.RuntimeState)\\n (state : IRState)\\n (helperFuel : Nat)\\n (irFuel : Nat),\\n 0 < helperFuel →\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\\n FunctionBody.scopeNamesPresent scope runtime.bindings →\\n FunctionBody.bindingsBounded runtime.bindings →\\n FunctionBody.runtimeStateMatchesIR fields runtime state →\\n stmtStepMatchesIRExecWithInternals fields\\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\\n (Stmt.internalCallAssign names calleeName args))\\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\\n [YulStmt.letMany names (YulExpr.call\\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\\n CompiledStmtStepWithHelpersAndHelperIR\\n runtimeContract spec fields scope\\n (Stmt.internalCallAssign names calleeName args)\\n compiledIR := by\\n refine {\\n compileOk := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n preserves := ?_ }\\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\\n have hArgEq : argExprs' = argExprs := by\\n simp [hargCompile] at hargOk\\n exact hargOk.symm\\n subst hArgEq\\n set singletonIR :=\\n [YulStmt.letMany names\\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\\n have hshape' : compiledIR = singletonIR := by\\n simpa [singletonIR] using hshape\\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\\n have hExtraPos : 1 ≤ extraFuel := by\\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\\n set irFuel := extraFuel - 1 with hirFuel\\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\\n rw [hlenOne, hirFuel]; omega\\n rw [hshape'] at hslack ⊢\\n rw [hlenOne] at hslack\\n rw [hFuelEq]\\n exact ⟨_, _, rfl, rfl, hMatch⟩\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 76,\n \"n_chars\": 3873,\n \"n_subproofs\": 9,\n \"n_tactics\": 34,\n \"cyclomatic\": 1,\n \"n_automation\": 10,\n \"n_rewrites\": 7,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"directInternalHelperHeadStepCatalog_of_bridgeCatalog","fan_in":2,"n_deps_direct":2,"n_deps_transitive":4,"n_lines":16,"n_chars":801,"n_subproofs":0,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"directInternalHelperHeadStepCatalog_of_bridgeCatalog\",\n \"fan_in\": 2,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 4,\n \"n_lines\": 16,\n \"n_chars\": 801,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":4,"string":"4"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by\n simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack\n rw [hlenOne] at hslack\n omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n (args := args) hmem with ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCall\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompileSpec\n hargCompile\n (hbridge.callBridge\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\nprivate theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := sorry\n\n/-- Build the reusable direct-helper head-step catalog from the lighter bridge\ncatalog seam. This keeps future helper-rank induction focused on exact singleton\nbridges instead of reconstructing `CompiledStmtStepWithHelpersAndHelperIR`\nobjects by hand at every theorem layer. -/\ntheorem directInternalHelperHeadStepCatalog_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · exact directInternalHelperHeadStepCatalog_call_of_bridgeCatalog hbridge\n · exact directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog hbridge\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\nsupply. The bridge captures the end-to-end obligation: given matching\npreconditions, the source and IR execution results for this statement match\nthrough `stmtStepMatchesIRExecWithInternals`.\n\nThe bridge is quantified over an extra `irFuel` so that the proof can\ninstantiate it at the right fuel level derived from `extraFuel`.\n\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by\n simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack\n rw [hlenOne] at hslack\n omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n (args := args) hmem with ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCall\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompileSpec\n hargCompile\n (hbridge.callBridge\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\nprivate theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n have hcompileSpec :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n hcompileSpec\n hargCompile\n (hbridge.assignBridge\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\n/-- Build the reusable direct-helper head-step catalog from the lighter bridge\ncatalog seam. This keeps future helper-rank induction focused on exact singleton\nbridges instead of reconstructing `CompiledStmtStepWithHelpersAndHelperIR`\nobjects by hand at every theorem layer. -/\ntheorem directInternalHelperHeadStepCatalog_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · exact directInternalHelperHeadStepCatalog_call_of_bridgeCatalog hbridge\n · exact directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog hbridge\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -10,6 +10,81 @@\n open Compiler.CompilationModel\n open Compiler.Yul\n \n+/-- Constructor for the helper-aware single-step interface when the head\n+statement is `Stmt.internalCallAssign`. The proof is parameterised by a single\n+source-to-IR alignment bridge that the rank-decreasing callee induction will\n+supply. The bridge captures the end-to-end obligation: given matching\n+preconditions, the source and IR execution results for this statement match\n+through `stmtStepMatchesIRExecWithInternals`.\n+\n+The bridge is quantified over an extra `irFuel` so that the proof can\n+instantiate it at the right fuel level derived from `extraFuel`.\n+\n+The `compileOk` obligation is passed through from the compilation hypothesis. -/\n+theorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n+ {runtimeContract : IRContract}\n+ {spec : CompilationModel}\n+ {fields : List Field}\n+ {scope : List String}\n+ {names : List String} {calleeName : String} {args : List Expr}\n+ {compiledIR : List YulStmt}\n+ {argExprs : List YulExpr}\n+ (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n+ (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n+ -- End-to-end source↔IR alignment bridge.\n+ (bridge :\n+ ∀ (runtime : SourceSemantics.RuntimeState)\n+ (state : IRState)\n+ (helperFuel : Nat)\n+ (irFuel : Nat),\n+ 0 < helperFuel →\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n+ FunctionBody.scopeNamesPresent scope runtime.bindings →\n+ FunctionBody.bindingsBounded runtime.bindings →\n+ FunctionBody.runtimeStateMatchesIR fields runtime state →\n+ stmtStepMatchesIRExecWithInternals fields\n+ (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n+ (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n+ (Stmt.internalCallAssign names calleeName args))\n+ (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n+ [YulStmt.letMany names (YulExpr.call\n+ (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n+ CompiledStmtStepWithHelpersAndHelperIR\n+ runtimeContract spec fields scope\n+ (Stmt.internalCallAssign names calleeName args)\n+ compiledIR := by\n+ refine {\n+ compileOk := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ preserves := ?_ }\n+ intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n+ have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n+ have hArgEq : argExprs' = argExprs := by\n+ simp [hargCompile] at hargOk\n+ exact hargOk.symm\n+ subst hArgEq\n+ set singletonIR :=\n+ [YulStmt.letMany names\n+ (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n+ have hshape' : compiledIR = singletonIR := by\n+ simpa [singletonIR] using hshape\n+ have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n+ have hExtraPos : 1 ≤ extraFuel := by\n+ have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n+ rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n+ set irFuel := extraFuel - 1 with hirFuel\n+ have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n+ have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n+ rw [hlenOne, hirFuel]; omega\n+ rw [hshape'] at hslack ⊢\n+ rw [hlenOne] at hslack\n+ rw [hFuelEq]\n+ exact ⟨_, _, rfl, rfl, hMatch⟩\n+\n theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n@@ -441,7 +516,30 @@\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n- compiledIR := sorry\n+ compiledIR := by\n+ intro scope names calleeName args hmem\n+ rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n+ ⟨compiledIR, hcompile⟩\n+ obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n+ have hcompileSpec :\n+ CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ refine ⟨compiledIR, ?_⟩\n+ exact\n+ compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n+ hcompileSpec\n+ hargCompile\n+ (hbridge.assignBridge\n+ (scope := scope)\n+ (names := names)\n+ (calleeName := calleeName)\n+ (args := args)\n+ (compiledIR := compiledIR)\n+ (argExprs := argExprs)\n+ hmem\n+ hcompile\n+ hargCompile)\n \n /-- Build the reusable direct-helper head-step catalog from the lighter bridge\n catalog seam. This keeps future helper-rank induction focused on exact singleton\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21359,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_6"},"challenge_id":{"kind":"string","value":"3c34c3ee1cfca0ef"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":6,"string":"6"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog","depth":1,"n_commands":0,"n_lines":24,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n have hcompileSpec :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n hcompileSpec\n hargCompile\n (hbridge.assignBridge\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)","n_chars":966,"n_subproofs":2,"n_tactics":24,"cyclomatic":2,"n_automation":1,"n_rewrites":0,"n_structural":5,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 24,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro scope names calleeName args hmem\\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\\n ⟨compiledIR, hcompile⟩\\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\\n have hcompileSpec :\\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n refine ⟨compiledIR, ?_⟩\\n exact\\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\\n hcompileSpec\\n hargCompile\\n (hbridge.assignBridge\\n (scope := scope)\\n (names := names)\\n (calleeName := calleeName)\\n (args := args)\\n (compiledIR := compiledIR)\\n (argExprs := argExprs)\\n hmem\\n hcompile\\n hargCompile)\",\n \"n_chars\": 966,\n \"n_subproofs\": 2,\n \"n_tactics\": 24,\n \"cyclomatic\": 2,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compiledStmtStepWithHelpersAndHelperIR_internalCallAssign","text":"/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\nsupply. The bridge captures the end-to-end obligation: given matching\npreconditions, the source and IR execution results for this statement match\nthrough `stmtStepMatchesIRExecWithInternals`.\n\nThe bridge is quantified over an extra `irFuel` so that the proof can\ninstantiate it at the right fuel level derived from `extraFuel`.\n\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n","fan_in":1,"n_lines":76,"n_chars":3873,"n_subproofs":9,"n_tactics":34,"cyclomatic":1,"n_automation":10,"n_rewrites":7,"n_structural":5,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\",\n \"text\": \"/-- Constructor for the helper-aware single-step interface when the head\\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\\nsupply. The bridge captures the end-to-end obligation: given matching\\npreconditions, the source and IR execution results for this statement match\\nthrough `stmtStepMatchesIRExecWithInternals`.\\n\\nThe bridge is quantified over an extra `irFuel` so that the proof can\\ninstantiate it at the right fuel level derived from `extraFuel`.\\n\\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\\n {runtimeContract : IRContract}\\n {spec : CompilationModel}\\n {fields : List Field}\\n {scope : List String}\\n {names : List String} {calleeName : String} {args : List Expr}\\n {compiledIR : List YulStmt}\\n {argExprs : List YulExpr}\\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\\n -- End-to-end source↔IR alignment bridge.\\n (bridge :\\n ∀ (runtime : SourceSemantics.RuntimeState)\\n (state : IRState)\\n (helperFuel : Nat)\\n (irFuel : Nat),\\n 0 < helperFuel →\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\\n FunctionBody.scopeNamesPresent scope runtime.bindings →\\n FunctionBody.bindingsBounded runtime.bindings →\\n FunctionBody.runtimeStateMatchesIR fields runtime state →\\n stmtStepMatchesIRExecWithInternals fields\\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\\n (Stmt.internalCallAssign names calleeName args))\\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\\n [YulStmt.letMany names (YulExpr.call\\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\\n CompiledStmtStepWithHelpersAndHelperIR\\n runtimeContract spec fields scope\\n (Stmt.internalCallAssign names calleeName args)\\n compiledIR := by\\n refine {\\n compileOk := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n preserves := ?_ }\\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\\n have hArgEq : argExprs' = argExprs := by\\n simp [hargCompile] at hargOk\\n exact hargOk.symm\\n subst hArgEq\\n set singletonIR :=\\n [YulStmt.letMany names\\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\\n have hshape' : compiledIR = singletonIR := by\\n simpa [singletonIR] using hshape\\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\\n have hExtraPos : 1 ≤ extraFuel := by\\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\\n set irFuel := extraFuel - 1 with hirFuel\\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\\n rw [hlenOne, hirFuel]; omega\\n rw [hshape'] at hslack ⊢\\n rw [hlenOne] at hslack\\n rw [hFuelEq]\\n exact ⟨_, _, rfl, rfl, hMatch⟩\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 76,\n \"n_chars\": 3873,\n \"n_subproofs\": 9,\n \"n_tactics\": 34,\n \"cyclomatic\": 1,\n \"n_automation\": 10,\n \"n_rewrites\": 7,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"directInternalHelperHeadStepCatalog_of_perCalleeBridgeCatalog","fan_in":0,"n_deps_direct":2,"n_deps_transitive":6,"n_lines":25,"n_chars":1044,"n_subproofs":0,"n_tactics":13,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"directInternalHelperHeadStepCatalog_of_perCalleeBridgeCatalog\",\n \"fan_in\": 0,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 6,\n \"n_lines\": 25,\n \"n_chars\": 1044,\n \"n_subproofs\": 0,\n \"n_tactics\": 13,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":6,"string":"6"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by\n simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack\n rw [hlenOne] at hslack\n omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\ntheorem directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hcallee : DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro scope calleeName args hmem\n exact (hcallee.call hmem).compile (scope := scope) (args := args)\n · intro scope calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.call hmem).bridge\n (scope := scope)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n · intro scope names calleeName args hmem\n exact (hcallee.assign hmem).compile (scope := scope) (names := names) (args := args)\n · intro scope names calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.assign hmem).bridge\n (scope := scope)\n (names := names)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n\nprivate theorem directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n (args := args) hmem with ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCall\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompileSpec\n hargCompile\n (hbridge.callBridge\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\nprivate theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := sorry\n\n/-- Build the reusable direct-helper head-step catalog from the lighter bridge\ncatalog seam. This keeps future helper-rank induction focused on exact singleton\nbridges instead of reconstructing `CompiledStmtStepWithHelpersAndHelperIR`\nobjects by hand at every theorem layer. -/\ntheorem directInternalHelperHeadStepCatalog_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · exact directInternalHelperHeadStepCatalog_call_of_bridgeCatalog hbridge\n · exact directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog hbridge\n\n/-- Assemble the reusable direct-helper head-step catalog directly from the more\nrank-induction-friendly per-callee bridge inventory. This lets downstream\nwrapper theorems consume the exact catalog object future rank induction should\nbuild, without routing through the intermediate body-level bridge catalog. -/\ntheorem directInternalHelperHeadStepCatalog_of_perCalleeBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hcallee : DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n exact\n directInternalHelperHeadStepCatalog_of_bridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n (directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n hcallee)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\nsupply. The bridge captures the end-to-end obligation: given matching\npreconditions, the source and IR execution results for this statement match\nthrough `stmtStepMatchesIRExecWithInternals`.\n\nThe bridge is quantified over an extra `irFuel` so that the proof can\ninstantiate it at the right fuel level derived from `extraFuel`.\n\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by\n simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack\n rw [hlenOne] at hslack\n omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\ntheorem directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hcallee : DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro scope calleeName args hmem\n exact (hcallee.call hmem).compile (scope := scope) (args := args)\n · intro scope calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.call hmem).bridge\n (scope := scope)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n · intro scope names calleeName args hmem\n exact (hcallee.assign hmem).compile (scope := scope) (names := names) (args := args)\n · intro scope names calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.assign hmem).bridge\n (scope := scope)\n (names := names)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n\nprivate theorem directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n (args := args) hmem with ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCall\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompileSpec\n hargCompile\n (hbridge.callBridge\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\nprivate theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n have hcompileSpec :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n hcompileSpec\n hargCompile\n (hbridge.assignBridge\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\n/-- Build the reusable direct-helper head-step catalog from the lighter bridge\ncatalog seam. This keeps future helper-rank induction focused on exact singleton\nbridges instead of reconstructing `CompiledStmtStepWithHelpersAndHelperIR`\nobjects by hand at every theorem layer. -/\ntheorem directInternalHelperHeadStepCatalog_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · exact directInternalHelperHeadStepCatalog_call_of_bridgeCatalog hbridge\n · exact directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog hbridge\n\n/-- Assemble the reusable direct-helper head-step catalog directly from the more\nrank-induction-friendly per-callee bridge inventory. This lets downstream\nwrapper theorems consume the exact catalog object future rank induction should\nbuild, without routing through the intermediate body-level bridge catalog. -/\ntheorem directInternalHelperHeadStepCatalog_of_perCalleeBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hcallee : DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n exact\n directInternalHelperHeadStepCatalog_of_bridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n (directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n hcallee)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -10,6 +10,81 @@\n open Compiler.CompilationModel\n open Compiler.Yul\n \n+/-- Constructor for the helper-aware single-step interface when the head\n+statement is `Stmt.internalCallAssign`. The proof is parameterised by a single\n+source-to-IR alignment bridge that the rank-decreasing callee induction will\n+supply. The bridge captures the end-to-end obligation: given matching\n+preconditions, the source and IR execution results for this statement match\n+through `stmtStepMatchesIRExecWithInternals`.\n+\n+The bridge is quantified over an extra `irFuel` so that the proof can\n+instantiate it at the right fuel level derived from `extraFuel`.\n+\n+The `compileOk` obligation is passed through from the compilation hypothesis. -/\n+theorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n+ {runtimeContract : IRContract}\n+ {spec : CompilationModel}\n+ {fields : List Field}\n+ {scope : List String}\n+ {names : List String} {calleeName : String} {args : List Expr}\n+ {compiledIR : List YulStmt}\n+ {argExprs : List YulExpr}\n+ (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n+ (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n+ -- End-to-end source↔IR alignment bridge.\n+ (bridge :\n+ ∀ (runtime : SourceSemantics.RuntimeState)\n+ (state : IRState)\n+ (helperFuel : Nat)\n+ (irFuel : Nat),\n+ 0 < helperFuel →\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n+ FunctionBody.scopeNamesPresent scope runtime.bindings →\n+ FunctionBody.bindingsBounded runtime.bindings →\n+ FunctionBody.runtimeStateMatchesIR fields runtime state →\n+ stmtStepMatchesIRExecWithInternals fields\n+ (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n+ (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n+ (Stmt.internalCallAssign names calleeName args))\n+ (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n+ [YulStmt.letMany names (YulExpr.call\n+ (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n+ CompiledStmtStepWithHelpersAndHelperIR\n+ runtimeContract spec fields scope\n+ (Stmt.internalCallAssign names calleeName args)\n+ compiledIR := by\n+ refine {\n+ compileOk := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ preserves := ?_ }\n+ intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n+ have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n+ have hArgEq : argExprs' = argExprs := by\n+ simp [hargCompile] at hargOk\n+ exact hargOk.symm\n+ subst hArgEq\n+ set singletonIR :=\n+ [YulStmt.letMany names\n+ (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n+ have hshape' : compiledIR = singletonIR := by\n+ simpa [singletonIR] using hshape\n+ have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n+ have hExtraPos : 1 ≤ extraFuel := by\n+ have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n+ rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n+ set irFuel := extraFuel - 1 with hirFuel\n+ have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n+ have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n+ rw [hlenOne, hirFuel]; omega\n+ rw [hshape'] at hslack ⊢\n+ rw [hlenOne] at hslack\n+ rw [hFuelEq]\n+ exact ⟨_, _, rfl, rfl, hMatch⟩\n+\n theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n@@ -471,7 +546,30 @@\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n- compiledIR := sorry\n+ compiledIR := by\n+ intro scope names calleeName args hmem\n+ rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n+ ⟨compiledIR, hcompile⟩\n+ obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n+ have hcompileSpec :\n+ CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n+ (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ refine ⟨compiledIR, ?_⟩\n+ exact\n+ compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n+ hcompileSpec\n+ hargCompile\n+ (hbridge.assignBridge\n+ (scope := scope)\n+ (names := names)\n+ (calleeName := calleeName)\n+ (args := args)\n+ (compiledIR := compiledIR)\n+ (argExprs := argExprs)\n+ hmem\n+ hcompile\n+ hargCompile)\n \n /-- Build the reusable direct-helper head-step catalog from the lighter bridge\n catalog seam. This keeps future helper-rank induction focused on exact singleton\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21360,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_7"},"challenge_id":{"kind":"string","value":"672800b91532c096"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":7,"string":"7"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"directInternalHelperHeadStepCatalog_call_of_bridgeCatalog","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n (args := args) hmem with ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCall\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompileSpec\n hargCompile\n (hbridge.callBridge\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)","n_chars":1120,"n_subproofs":2,"n_tactics":31,"cyclomatic":2,"n_automation":1,"n_rewrites":0,"n_structural":5,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n intro scope calleeName args hmem\\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\\n (args := args) hmem with ⟨compiledIR, hcompile⟩\\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\\n Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n refine ⟨compiledIR, ?_⟩\\n exact\\n compiledStmtStepWithHelpersAndHelperIR_internalCall\\n (runtimeContract := runtimeContract)\\n (spec := spec)\\n (fields := fields)\\n (scope := scope)\\n (calleeName := calleeName)\\n (args := args)\\n (compiledIR := compiledIR)\\n (argExprs := argExprs)\\n hcompileSpec\\n hargCompile\\n (hbridge.callBridge\\n (scope := scope)\\n (calleeName := calleeName)\\n (args := args)\\n (compiledIR := compiledIR)\\n (argExprs := argExprs)\\n hmem\\n hcompile\\n hargCompile)\",\n \"n_chars\": 1120,\n \"n_subproofs\": 2,\n \"n_tactics\": 31,\n \"cyclomatic\": 2,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compiledStmtStepWithHelpersAndHelperIR_internalCall","text":"theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by\n simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack\n rw [hlenOne] at hslack\n omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n","fan_in":1,"n_lines":68,"n_chars":3140,"n_subproofs":9,"n_tactics":35,"cyclomatic":1,"n_automation":10,"n_rewrites":7,"n_structural":5,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compiledStmtStepWithHelpersAndHelperIR_internalCall\",\n \"text\": \"theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\\n {runtimeContract : IRContract}\\n {spec : CompilationModel}\\n {fields : List Field}\\n {scope : List String}\\n {calleeName : String} {args : List Expr}\\n {compiledIR : List YulStmt}\\n {argExprs : List YulExpr}\\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\\n -- End-to-end source↔IR alignment bridge.\\n (bridge :\\n ∀ (runtime : SourceSemantics.RuntimeState)\\n (state : IRState)\\n (helperFuel : Nat)\\n (irFuel : Nat),\\n 0 < helperFuel →\\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\\n FunctionBody.scopeNamesPresent scope runtime.bindings →\\n FunctionBody.bindingsBounded runtime.bindings →\\n FunctionBody.runtimeStateMatchesIR fields runtime state →\\n stmtStepMatchesIRExecWithInternals fields\\n (stmtNextScope scope (Stmt.internalCall calleeName args))\\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\\n (Stmt.internalCall calleeName args))\\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\\n [YulStmt.exprStmt (YulExpr.call\\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\\n CompiledStmtStepWithHelpersAndHelperIR\\n runtimeContract spec fields scope\\n (Stmt.internalCall calleeName args)\\n compiledIR := by\\n refine {\\n compileOk := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n preserves := ?_ }\\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\\n have hArgEq : argExprs' = argExprs := by\\n simp [hargCompile] at hargOk\\n exact hargOk.symm\\n subst hArgEq\\n set singletonIR :=\\n [YulStmt.exprStmt\\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\\n have hshape' : compiledIR = singletonIR := by\\n simpa [singletonIR] using hshape\\n have hlenOne : singletonIR.length = 1 := by\\n simp [singletonIR]\\n have hExtraPos : 1 ≤ extraFuel := by\\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\\n rw [hshape'] at hslack\\n rw [hlenOne] at hslack\\n omega\\n set irFuel := extraFuel - 1 with hirFuel\\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\\n rw [hlenOne, hirFuel]; omega\\n rw [hshape'] at hslack ⊢\\n rw [hlenOne] at hslack\\n rw [hFuelEq]\\n exact ⟨_, _, rfl, rfl, hMatch⟩\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 68,\n \"n_chars\": 3140,\n \"n_subproofs\": 9,\n \"n_tactics\": 35,\n \"cyclomatic\": 1,\n \"n_automation\": 10,\n \"n_rewrites\": 7,\n \"n_structural\": 5,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"directInternalHelperHeadStepCatalog_of_supportedBody_and_assignBridgeCatalog","fan_in":0,"n_deps_direct":2,"n_deps_transitive":8,"n_lines":28,"n_chars":1096,"n_subproofs":0,"n_tactics":14,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"directInternalHelperHeadStepCatalog_of_supportedBody_and_assignBridgeCatalog\",\n \"fan_in\": 0,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 8,\n \"n_lines\": 28,\n \"n_chars\": 1096,\n \"n_subproofs\": 0,\n \"n_tactics\": 14,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":8,"string":"8"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\nsupply. The bridge captures the end-to-end obligation: given matching\npreconditions, the source and IR execution results for this statement match\nthrough `stmtStepMatchesIRExecWithInternals`.\n\nThe bridge is quantified over an extra `irFuel` so that the proof can\ninstantiate it at the right fuel level derived from `extraFuel`.\n\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Reassemble the full callee-local bridge catalog from the current supported\nbody witness plus the assign-only bridge half. The call half is vacuous because\n`SupportedStmtList` still excludes direct helper calls from the fragment. -/\ntheorem directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · intro calleeName hmem\n exfalso\n simp [hbody.helperCallNames_nil] at hmem\n · intro calleeName hmem\n exact hassign.assign hmem\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\ntheorem directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hcallee : DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro scope calleeName args hmem\n exact (hcallee.call hmem).compile (scope := scope) (args := args)\n · intro scope calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.call hmem).bridge\n (scope := scope)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n · intro scope names calleeName args hmem\n exact (hcallee.assign hmem).compile (scope := scope) (names := names) (args := args)\n · intro scope names calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.assign hmem).bridge\n (scope := scope)\n (names := names)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n\n/-- Assemble the body-level direct-helper bridge catalog directly from the\ncurrent helper-free supported-body witness plus the assign-only per-callee\nbridge inventory. This keeps downstream theorems on the exact assign-only Tier 4\nboundary instead of routing through the vacuous per-callee void-call layer. -/\ntheorem directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n exact\n directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n (directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n hbody\n hassign)\n\nprivate theorem directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR := sorry\n\nprivate theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n have hcompileSpec :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n hcompileSpec\n hargCompile\n (hbridge.assignBridge\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\n/-- Build the reusable direct-helper head-step catalog from the lighter bridge\ncatalog seam. This keeps future helper-rank induction focused on exact singleton\nbridges instead of reconstructing `CompiledStmtStepWithHelpersAndHelperIR`\nobjects by hand at every theorem layer. -/\ntheorem directInternalHelperHeadStepCatalog_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · exact directInternalHelperHeadStepCatalog_call_of_bridgeCatalog hbridge\n · exact directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog hbridge\n\n/-- Assemble the exact body-level direct-helper head-step catalog directly from\nthe split compile/semantic Tier 4 inventories. This removes the last per-callee\nbridge detour once callers already provide the compile catalog and semantic\nbridge data separately. -/\ntheorem directInternalHelperHeadStepCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n exact\n directInternalHelperHeadStepCatalog_of_bridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n (directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n hbody\n hassign)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction will\nsupply. The bridge captures the end-to-end obligation: given matching\npreconditions, the source and IR execution results for this statement match\nthrough `stmtStepMatchesIRExecWithInternals`.\n\nThe bridge is quantified over an extra `irFuel` so that the proof can\ninstantiate it at the right fuel level derived from `extraFuel`.\n\nThe `compileOk` obligation is passed through from the compilation hypothesis. -/\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCallAssign_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.letMany names\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack; rw [hlenOne] at hslack; omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\ntheorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt}\n {argExprs : List YulExpr}\n (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n -- End-to-end source↔IR alignment bridge.\n (bridge :\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n refine {\n compileOk := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n preserves := ?_ }\n intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n have hArgEq : argExprs' = argExprs := by\n simp [hargCompile] at hargOk\n exact hargOk.symm\n subst hArgEq\n set singletonIR :=\n [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n have hshape' : compiledIR = singletonIR := by\n simpa [singletonIR] using hshape\n have hlenOne : singletonIR.length = 1 := by\n simp [singletonIR]\n have hExtraPos : 1 ≤ extraFuel := by\n have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n rw [hshape'] at hslack\n rw [hlenOne] at hslack\n omega\n set irFuel := extraFuel - 1 with hirFuel\n have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n rw [hlenOne, hirFuel]; omega\n rw [hshape'] at hslack ⊢\n rw [hlenOne] at hslack\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Reassemble the full callee-local bridge catalog from the current supported\nbody witness plus the assign-only bridge half. The call half is vacuous because\n`SupportedStmtList` still excludes direct helper calls from the fragment. -/\ntheorem directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · intro calleeName hmem\n exfalso\n simp [hbody.helperCallNames_nil] at hmem\n · intro calleeName hmem\n exact hassign.assign hmem\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\ntheorem directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hcallee : DirectInternalHelperPerCalleeBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_, ?_, ?_⟩\n · intro scope calleeName args hmem\n exact (hcallee.call hmem).compile (scope := scope) (args := args)\n · intro scope calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.call hmem).bridge\n (scope := scope)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n · intro scope names calleeName args hmem\n exact (hcallee.assign hmem).compile (scope := scope) (names := names) (args := args)\n · intro scope names calleeName args compiledIR argExprs hmem hcompile hargCompile\n exact (hcallee.assign hmem).bridge\n (scope := scope)\n (names := names)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompile\n hargCompile\n\n/-- Assemble the body-level direct-helper bridge catalog directly from the\ncurrent helper-free supported-body witness plus the assign-only per-callee\nbridge inventory. This keeps downstream theorems on the exact assign-only Tier 4\nboundary instead of routing through the vacuous per-callee void-call layer. -/\ntheorem directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn := by\n exact\n directInternalHelperHeadStepBridgeCatalog_of_perCalleeBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n (directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n hbody\n hassign)\n\nprivate theorem directInternalHelperHeadStepCatalog_call_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR := by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n (args := args) hmem with ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCall\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hcompileSpec\n hargCompile\n (hbridge.callBridge\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\nprivate theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR := by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope := scope) (names := names) (calleeName := calleeName) (args := args) hmem with\n ⟨compiledIR, hcompile⟩\n obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCallAssign_shape hcompile\n have hcompileSpec :\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR := by\n simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n refine ⟨compiledIR, ?_⟩\n exact\n compiledStmtStepWithHelpersAndHelperIR_internalCallAssign\n hcompileSpec\n hargCompile\n (hbridge.assignBridge\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n (argExprs := argExprs)\n hmem\n hcompile\n hargCompile)\n\n/-- Build the reusable direct-helper head-step catalog from the lighter bridge\ncatalog seam. This keeps future helper-rank induction focused on exact singleton\nbridges instead of reconstructing `CompiledStmtStepWithHelpersAndHelperIR`\nobjects by hand at every theorem layer. -/\ntheorem directInternalHelperHeadStepCatalog_of_bridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbridge : DirectInternalHelperHeadStepBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n refine ⟨?_, ?_⟩\n · exact directInternalHelperHeadStepCatalog_call_of_bridgeCatalog hbridge\n · exact directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog hbridge\n\n/-- Assemble the exact body-level direct-helper head-step catalog directly from\nthe split compile/semantic Tier 4 inventories. This removes the last per-callee\nbridge detour once callers already provide the compile catalog and semantic\nbridge data separately. -/\ntheorem directInternalHelperHeadStepCatalog_of_supportedBody_and_assignBridgeCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {fn : FunctionSpec}\n (hbody : SupportedBodyInterface spec fn)\n (hassign :\n DirectInternalHelperPerCalleeAssignBridgeCatalog runtimeContract spec fields fn) :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn := by\n exact\n directInternalHelperHeadStepCatalog_of_bridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n (directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (fn := fn)\n hbody\n hassign)\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -85,6 +85,73 @@\n rw [hFuelEq]\n exact ⟨_, _, rfl, rfl, hMatch⟩\n \n+theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n+ {runtimeContract : IRContract}\n+ {spec : CompilationModel}\n+ {fields : List Field}\n+ {scope : List String}\n+ {calleeName : String} {args : List Expr}\n+ {compiledIR : List YulStmt}\n+ {argExprs : List YulExpr}\n+ (hcompile : CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n+ (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n+ (hargCompile : CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n+ -- End-to-end source↔IR alignment bridge.\n+ (bridge :\n+ ∀ (runtime : SourceSemantics.RuntimeState)\n+ (state : IRState)\n+ (helperFuel : Nat)\n+ (irFuel : Nat),\n+ 0 < helperFuel →\n+ FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n+ FunctionBody.scopeNamesPresent scope runtime.bindings →\n+ FunctionBody.bindingsBounded runtime.bindings →\n+ FunctionBody.runtimeStateMatchesIR fields runtime state →\n+ stmtStepMatchesIRExecWithInternals fields\n+ (stmtNextScope scope (Stmt.internalCall calleeName args))\n+ (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n+ (Stmt.internalCall calleeName args))\n+ (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n+ [YulStmt.exprStmt (YulExpr.call\n+ (CompilationModel.internalFunctionYulName calleeName) argExprs)])) :\n+ CompiledStmtStepWithHelpersAndHelperIR\n+ runtimeContract spec fields scope\n+ (Stmt.internalCall calleeName args)\n+ compiledIR := by\n+ refine {\n+ compileOk := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ preserves := ?_ }\n+ intro runtime state helperFuel extraFuel hfuelPos hexact hscope hbounded hruntime hslack\n+ have hcompileEmpty : CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n+ (Stmt.internalCall calleeName args) = Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ obtain ⟨argExprs', hargOk, hshape⟩ := compileStmt_internalCall_shape hcompileEmpty\n+ have hArgEq : argExprs' = argExprs := by\n+ simp [hargCompile] at hargOk\n+ exact hargOk.symm\n+ subst hArgEq\n+ set singletonIR :=\n+ [YulStmt.exprStmt\n+ (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs')]\n+ have hshape' : compiledIR = singletonIR := by\n+ simpa [singletonIR] using hshape\n+ have hlenOne : singletonIR.length = 1 := by\n+ simp [singletonIR]\n+ have hExtraPos : 1 ≤ extraFuel := by\n+ have hsz : sizeOf singletonIR ≥ 2 := by simp [singletonIR]\n+ rw [hshape'] at hslack\n+ rw [hlenOne] at hslack\n+ omega\n+ set irFuel := extraFuel - 1 with hirFuel\n+ have hMatch := bridge runtime state helperFuel irFuel hfuelPos hexact hscope hbounded hruntime\n+ have hFuelEq : singletonIR.length + extraFuel + 1 = irFuel + 3 := by\n+ rw [hlenOne, hirFuel]; omega\n+ rw [hshape'] at hslack ⊢\n+ rw [hlenOne] at hslack\n+ rw [hFuelEq]\n+ exact ⟨_, _, rfl, rfl, hMatch⟩\n+\n /-- Exact Tier 4 head-step proof object for a function body's direct internal\n helper surface. Future helper-rank induction should construct this single\n catalog once, then reuse the mechanical list-interface assembly theorems\n@@ -478,7 +545,37 @@\n fields\n scope\n (Stmt.internalCall calleeName args)\n- compiledIR := sorry\n+ compiledIR := by\n+ intro scope calleeName args hmem\n+ rcases hbridge.callCompile (scope := scope) (calleeName := calleeName)\n+ (args := args) hmem with ⟨compiledIR, hcompile⟩\n+ obtain ⟨argExprs, hargCompile, _⟩ := compileStmt_internalCall_shape hcompile\n+ have hcompileSpec : CompilationModel.compileStmt fields spec.events spec.errors\n+ .calldata [] false scope [] (Stmt.internalCall calleeName args) =\n+ Except.ok compiledIR := by\n+ simpa [CompilationModel.compileStmt, CompilationModel.compileStmtWithFork] using hcompile\n+ refine ⟨compiledIR, ?_⟩\n+ exact\n+ compiledStmtStepWithHelpersAndHelperIR_internalCall\n+ (runtimeContract := runtimeContract)\n+ (spec := spec)\n+ (fields := fields)\n+ (scope := scope)\n+ (calleeName := calleeName)\n+ (args := args)\n+ (compiledIR := compiledIR)\n+ (argExprs := argExprs)\n+ hcompileSpec\n+ hargCompile\n+ (hbridge.callBridge\n+ (scope := scope)\n+ (calleeName := calleeName)\n+ (args := args)\n+ (compiledIR := compiledIR)\n+ (argExprs := argExprs)\n+ hmem\n+ hcompile\n+ hargCompile)\n \n private theorem directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog\n {runtimeContract : IRContract}\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21361,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_8"},"challenge_id":{"kind":"string","value":"bb11eb2e42eabf20"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":8,"string":"8"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_iff_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a","n_chars":69,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_iff_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\",\n \"n_chars\": 69,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"eraseDups_nodup_and_mem_aux_local","text":"private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\n","fan_in":1,"n_lines":43,"n_chars":1642,"n_subproofs":6,"n_tactics":39,"cyclomatic":8,"n_automation":8,"n_rewrites":6,"n_structural":18,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"eraseDups_nodup_and_mem_aux_local\",\n \"text\": \"private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\\n induction n generalizing l with\\n | zero =>\\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\\n subst this\\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\\n | succ n ih =>\\n match l with\\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\\n | x :: xs =>\\n rw [List.eraseDups_cons]\\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\\n have := List.length_filter_le (fun b => !b == x) xs\\n simp [List.length_cons] at hlen\\n omega\\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\\n constructor\\n · rw [List.nodup_cons]\\n constructor\\n · intro h\\n have hmf := (ihMem x).mp h\\n rw [List.mem_filter] at hmf\\n have := hmf.2\\n simp at this\\n · exact ihNd\\n · intro a\\n constructor\\n · intro h\\n rw [List.mem_cons] at h ⊢\\n rcases h with rfl | h\\n · exact Or.inl rfl\\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\\n · intro h\\n rw [List.mem_cons] at h ⊢\\n rcases h with rfl | h\\n · exact Or.inl rfl\\n · by_cases heq : a == x\\n · exact Or.inl (beq_iff_eq.mp heq)\\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 43,\n \"n_chars\": 1642,\n \"n_subproofs\": 6,\n \"n_tactics\": 39,\n \"cyclomatic\": 8,\n \"n_automation\": 8,\n \"n_rewrites\": 6,\n \"n_structural\": 18,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"List.mem_eraseDups_iff_local","fan_in":2,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":5,"n_chars":201,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_iff_local\",\n \"fan_in\": 2,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 5,\n \"n_chars\": 201,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l := sorry\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -312,8 +312,51 @@\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n \n+private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n+ (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n+ (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n+ induction n generalizing l with\n+ | zero =>\n+ have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n+ subst this\n+ exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n+ | succ n ih =>\n+ match l with\n+ | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n+ | x :: xs =>\n+ rw [List.eraseDups_cons]\n+ have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n+ have := List.length_filter_le (fun b => !b == x) xs\n+ simp [List.length_cons] at hlen\n+ omega\n+ have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n+ constructor\n+ · rw [List.nodup_cons]\n+ constructor\n+ · intro h\n+ have hmf := (ihMem x).mp h\n+ rw [List.mem_filter] at hmf\n+ have := hmf.2\n+ simp at this\n+ · exact ihNd\n+ · intro a\n+ constructor\n+ · intro h\n+ rw [List.mem_cons] at h ⊢\n+ rcases h with rfl | h\n+ · exact Or.inl rfl\n+ · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n+ · intro h\n+ rw [List.mem_cons] at h ⊢\n+ rcases h with rfl | h\n+ · exact Or.inl rfl\n+ · by_cases heq : a == x\n+ · exact Or.inl (beq_iff_eq.mp heq)\n+ · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n+\n private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l := sorry\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n \n end Compiler.Proofs.IRGeneration\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21362,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_9"},"challenge_id":{"kind":"string","value":"9a5348957a453fcb"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":9,"string":"9"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_iff_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a","n_chars":69,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_iff_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\",\n \"n_chars\": 69,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"eraseDups_nodup_and_mem_aux_local","text":"private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\n","fan_in":1,"n_lines":43,"n_chars":1642,"n_subproofs":6,"n_tactics":39,"cyclomatic":8,"n_automation":8,"n_rewrites":6,"n_structural":18,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"eraseDups_nodup_and_mem_aux_local\",\n \"text\": \"private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\\n induction n generalizing l with\\n | zero =>\\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\\n subst this\\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\\n | succ n ih =>\\n match l with\\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\\n | x :: xs =>\\n rw [List.eraseDups_cons]\\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\\n have := List.length_filter_le (fun b => !b == x) xs\\n simp [List.length_cons] at hlen\\n omega\\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\\n constructor\\n · rw [List.nodup_cons]\\n constructor\\n · intro h\\n have hmf := (ihMem x).mp h\\n rw [List.mem_filter] at hmf\\n have := hmf.2\\n simp at this\\n · exact ihNd\\n · intro a\\n constructor\\n · intro h\\n rw [List.mem_cons] at h ⊢\\n rcases h with rfl | h\\n · exact Or.inl rfl\\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\\n · intro h\\n rw [List.mem_cons] at h ⊢\\n rcases h with rfl | h\\n · exact Or.inl rfl\\n · by_cases heq : a == x\\n · exact Or.inl (beq_iff_eq.mp heq)\\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 43,\n \"n_chars\": 1642,\n \"n_subproofs\": 6,\n \"n_tactics\": 39,\n \"cyclomatic\": 8,\n \"n_automation\": 8,\n \"n_rewrites\": 6,\n \"n_structural\": 18,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"List.mem_eraseDups_of_mem_local","fan_in":6,"n_deps_direct":1,"n_deps_transitive":2,"n_lines":5,"n_chars":174,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_of_mem_local\",\n \"fan_in\": 6,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 2,\n \"n_lines\": 5,\n \"n_chars\": 174,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l := sorry\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -312,8 +312,51 @@\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n \n+private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n+ (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n+ (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n+ induction n generalizing l with\n+ | zero =>\n+ have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n+ subst this\n+ exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n+ | succ n ih =>\n+ match l with\n+ | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n+ | x :: xs =>\n+ rw [List.eraseDups_cons]\n+ have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n+ have := List.length_filter_le (fun b => !b == x) xs\n+ simp [List.length_cons] at hlen\n+ omega\n+ have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n+ constructor\n+ · rw [List.nodup_cons]\n+ constructor\n+ · intro h\n+ have hmf := (ihMem x).mp h\n+ rw [List.mem_filter] at hmf\n+ have := hmf.2\n+ simp at this\n+ · exact ihNd\n+ · intro a\n+ constructor\n+ · intro h\n+ rw [List.mem_cons] at h ⊢\n+ rcases h with rfl | h\n+ · exact Or.inl rfl\n+ · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n+ · intro h\n+ rw [List.mem_cons] at h ⊢\n+ rcases h with rfl | h\n+ · exact Or.inl rfl\n+ · by_cases heq : a == x\n+ · exact Or.inl (beq_iff_eq.mp heq)\n+ · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n+\n private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l := sorry\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n \n private theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21363,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_10"},"challenge_id":{"kind":"string","value":"c7feacdc436bfb62"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":10,"string":"10"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_iff_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a","n_chars":69,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_iff_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\",\n \"n_chars\": 69,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"eraseDups_nodup_and_mem_aux_local","text":"private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\n","fan_in":1,"n_lines":43,"n_chars":1642,"n_subproofs":6,"n_tactics":39,"cyclomatic":8,"n_automation":8,"n_rewrites":6,"n_structural":18,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"eraseDups_nodup_and_mem_aux_local\",\n \"text\": \"private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\\n induction n generalizing l with\\n | zero =>\\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\\n subst this\\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\\n | succ n ih =>\\n match l with\\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\\n | x :: xs =>\\n rw [List.eraseDups_cons]\\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\\n have := List.length_filter_le (fun b => !b == x) xs\\n simp [List.length_cons] at hlen\\n omega\\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\\n constructor\\n · rw [List.nodup_cons]\\n constructor\\n · intro h\\n have hmf := (ihMem x).mp h\\n rw [List.mem_filter] at hmf\\n have := hmf.2\\n simp at this\\n · exact ihNd\\n · intro a\\n constructor\\n · intro h\\n rw [List.mem_cons] at h ⊢\\n rcases h with rfl | h\\n · exact Or.inl rfl\\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\\n · intro h\\n rw [List.mem_cons] at h ⊢\\n rcases h with rfl | h\\n · exact Or.inl rfl\\n · by_cases heq : a == x\\n · exact Or.inl (beq_iff_eq.mp heq)\\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 43,\n \"n_chars\": 1642,\n \"n_subproofs\": 6,\n \"n_tactics\": 39,\n \"cyclomatic\": 8,\n \"n_automation\": 8,\n \"n_rewrites\": 6,\n \"n_structural\": 18,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"List.mem_of_mem_eraseDups_local","fan_in":4,"n_deps_direct":1,"n_deps_transitive":2,"n_lines":5,"n_chars":173,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_of_mem_eraseDups_local\",\n \"fan_in\": 4,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 2,\n \"n_lines\": 5,\n \"n_chars\": 173,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l := sorry\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n List.mem_eraseDups_iff_local.mp h\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n List.mem_eraseDups_iff_local.mp h\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -312,8 +312,51 @@\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n \n+private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n+ (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n+ (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n+ induction n generalizing l with\n+ | zero =>\n+ have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n+ subst this\n+ exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n+ | succ n ih =>\n+ match l with\n+ | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n+ | x :: xs =>\n+ rw [List.eraseDups_cons]\n+ have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n+ have := List.length_filter_le (fun b => !b == x) xs\n+ simp [List.length_cons] at hlen\n+ omega\n+ have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n+ constructor\n+ · rw [List.nodup_cons]\n+ constructor\n+ · intro h\n+ have hmf := (ihMem x).mp h\n+ rw [List.mem_filter] at hmf\n+ have := hmf.2\n+ simp at this\n+ · exact ihNd\n+ · intro a\n+ constructor\n+ · intro h\n+ rw [List.mem_cons] at h ⊢\n+ rcases h with rfl | h\n+ · exact Or.inl rfl\n+ · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n+ · intro h\n+ rw [List.mem_cons] at h ⊢\n+ rcases h with rfl | h\n+ · exact Or.inl rfl\n+ · by_cases heq : a == x\n+ · exact Or.inl (beq_iff_eq.mp heq)\n+ · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n+\n private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l := sorry\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n \n private theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21364,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_11"},"challenge_id":{"kind":"string","value":"e545161a59d2cff9"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":11,"string":"11"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_of_mem_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mpr h","n_chars":37,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2},{"theorem_name":"List.mem_of_mem_eraseDups_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mp h","n_chars":36,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_of_mem_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mpr h\",\n \"n_chars\": 37,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n },\n {\n \"theorem_name\": \"List.mem_of_mem_eraseDups_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mp h\",\n \"n_chars\": 36,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"List.mem_eraseDups_iff_local","text":"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n","fan_in":2,"n_lines":5,"n_chars":201,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_iff_local\",\n \"text\": \"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 201,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups","fan_in":2,"n_deps_direct":1,"n_deps_transitive":3,"n_lines":9,"n_chars":426,"n_subproofs":0,"n_tactics":3,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\",\n \"fan_in\": 2,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 3,\n \"n_lines\": 9,\n \"n_chars\": 426,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n\nprivate theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCallAssign names calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nprivate theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCallAssign names calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -354,8 +354,13 @@\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n \n+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n+\n private theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n+ {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n+ List.mem_eraseDups_iff_local.mpr h\n \n private theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21365,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_12"},"challenge_id":{"kind":"string","value":"3d16e9a01f47c819"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":12,"string":"12"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_of_mem_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mpr h","n_chars":37,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2},{"theorem_name":"List.mem_of_mem_eraseDups_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mp h","n_chars":36,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_of_mem_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mpr h\",\n \"n_chars\": 37,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n },\n {\n \"theorem_name\": \"List.mem_of_mem_eraseDups_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mp h\",\n \"n_chars\": 36,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"List.mem_eraseDups_iff_local","text":"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n","fan_in":2,"n_lines":5,"n_chars":201,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_iff_local\",\n \"text\": \"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 201,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups","fan_in":2,"n_deps_direct":1,"n_deps_transitive":3,"n_lines":9,"n_chars":386,"n_subproofs":0,"n_tactics":3,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\",\n \"fan_in\": 2,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 3,\n \"n_lines\": 9,\n \"n_chars\": 386,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n\nprivate theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCall calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nprivate theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCall calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -354,8 +354,13 @@\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n \n+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n+\n private theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n+ {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n+ List.mem_eraseDups_iff_local.mpr h\n \n private theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21366,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_13"},"challenge_id":{"kind":"string","value":"2e174c74ec950127"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":13,"string":"13"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_of_mem_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mpr h","n_chars":37,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2},{"theorem_name":"List.mem_of_mem_eraseDups_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mp h","n_chars":36,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_of_mem_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mpr h\",\n \"n_chars\": 37,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n },\n {\n \"theorem_name\": \"List.mem_of_mem_eraseDups_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mp h\",\n \"n_chars\": 36,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"List.mem_eraseDups_iff_local","text":"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n","fan_in":2,"n_lines":5,"n_chars":201,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_iff_local\",\n \"text\": \"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 201,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames","fan_in":1,"n_deps_direct":4,"n_deps_transitive":6,"n_lines":47,"n_chars":2126,"n_subproofs":1,"n_tactics":26,"cyclomatic":4,"n_automation":1,"n_rewrites":0,"n_structural":10,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames\",\n \"fan_in\": 1,\n \"n_deps_direct\": 4,\n \"n_deps_transitive\": 6,\n \"n_lines\": 47,\n \"n_chars\": 2126,\n \"n_subproofs\": 1,\n \"n_tactics\": 26,\n \"cyclomatic\": 4,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":6,"string":"6"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n\nprivate theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCallAssign names calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact direct-helper-assign list interface from head-step\nconstructors indexed only by helper callees that actually occur in the current\nstatement list. This is the precise seam future helper-rank induction should\ntarget: it no longer needs to quantify over arbitrary helper names unrelated to\nthe body under proof. -/\ntheorem stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperAssignStepInterface runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCallAssign names calleeName args =>\n rcases hstep\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperAssignSurface] at hdirect\n · apply ih\n intro scope names calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (names := names) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n List.mem_eraseDups_iff_local.mp h\n\nprivate theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCallAssign names calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact direct-helper-assign list interface from head-step\nconstructors indexed only by helper callees that actually occur in the current\nstatement list. This is the precise seam future helper-rank induction should\ntarget: it no longer needs to quantify over arbitrary helper names unrelated to\nthe body under proof. -/\ntheorem stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperAssignStepInterface runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCallAssign names calleeName args =>\n rcases hstep\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperAssignSurface] at hdirect\n · apply ih\n intro scope names calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (names := names) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -354,11 +354,17 @@\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n \n+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n+\n private theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n+ {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n+ List.mem_eraseDups_iff_local.mpr h\n \n private theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n+ {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n+ List.mem_eraseDups_iff_local.mp h\n \n private theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21367,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_14"},"challenge_id":{"kind":"string","value":"104c98436ee856c5"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":14,"string":"14"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_of_mem_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mpr h","n_chars":37,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2},{"theorem_name":"List.mem_of_mem_eraseDups_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mp h","n_chars":36,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_of_mem_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mpr h\",\n \"n_chars\": 37,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n },\n {\n \"theorem_name\": \"List.mem_of_mem_eraseDups_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mp h\",\n \"n_chars\": 36,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"List.mem_eraseDups_iff_local","text":"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n","fan_in":2,"n_lines":5,"n_chars":201,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_iff_local\",\n \"text\": \"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 201,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListDirectInternalHelperAssignStepInterfaceWithInternals_of_internalCallAssignSteps_of_helperCallNames","fan_in":0,"n_deps_direct":4,"n_deps_transitive":6,"n_lines":45,"n_chars":1994,"n_subproofs":1,"n_tactics":26,"cyclomatic":4,"n_automation":1,"n_rewrites":0,"n_structural":10,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"stmtListDirectInternalHelperAssignStepInterfaceWithInternals_of_internalCallAssignSteps_of_helperCallNames\",\n \"fan_in\": 0,\n \"n_deps_direct\": 4,\n \"n_deps_transitive\": 6,\n \"n_lines\": 45,\n \"n_chars\": 1994,\n \"n_subproofs\": 1,\n \"n_tactics\": 26,\n \"cyclomatic\": 4,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":6,"string":"6"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n\nprivate theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCallAssign names calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact `WithInternals` direct-helper-assign list interface from\nhead-step constructors indexed only by helper callees in the current list. -/\ntheorem stmtListDirectInternalHelperAssignStepInterfaceWithInternals_of_internalCallAssignSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperAssignStepInterfaceWithInternals\n runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCallAssign names calleeName args =>\n rcases hstep\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperAssignSurface] at hdirect\n · apply ih\n intro scope names calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (names := names) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n List.mem_eraseDups_iff_local.mp h\n\nprivate theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCallAssign names calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact `WithInternals` direct-helper-assign list interface from\nhead-step constructors indexed only by helper callees in the current list. -/\ntheorem stmtListDirectInternalHelperAssignStepInterfaceWithInternals_of_internalCallAssignSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperAssignStepInterfaceWithInternals\n runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCallAssign names calleeName args =>\n rcases hstep\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperAssignSurface] at hdirect\n · apply ih\n intro scope names calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (names := names) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -354,11 +354,17 @@\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n \n+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n+\n private theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n+ {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n+ List.mem_eraseDups_iff_local.mpr h\n \n private theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n+ {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n+ List.mem_eraseDups_iff_local.mp h\n \n private theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21368,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_15"},"challenge_id":{"kind":"string","value":"dca9d33483f4947f"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":15,"string":"15"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_of_mem_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mpr h","n_chars":37,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2},{"theorem_name":"List.mem_of_mem_eraseDups_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mp h","n_chars":36,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_of_mem_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mpr h\",\n \"n_chars\": 37,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n },\n {\n \"theorem_name\": \"List.mem_of_mem_eraseDups_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mp h\",\n \"n_chars\": 36,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"List.mem_eraseDups_iff_local","text":"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n","fan_in":2,"n_lines":5,"n_chars":201,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_iff_local\",\n \"text\": \"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 201,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames","fan_in":1,"n_deps_direct":4,"n_deps_transitive":6,"n_lines":46,"n_chars":2013,"n_subproofs":1,"n_tactics":25,"cyclomatic":4,"n_automation":1,"n_rewrites":0,"n_structural":10,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames\",\n \"fan_in\": 1,\n \"n_deps_direct\": 4,\n \"n_deps_transitive\": 6,\n \"n_lines\": 46,\n \"n_chars\": 2013,\n \"n_subproofs\": 1,\n \"n_tactics\": 25,\n \"cyclomatic\": 4,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":6,"string":"6"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n\nprivate theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCall calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact direct-helper-call list interface from head-step\nconstructors indexed only by helper callees that actually occur in the current\nstatement list. This matches the `helperCallNames`-based rank inventory carried\nby `SupportedBodyHelperInterface`, avoiding arbitrary-name quantification at the\nfunction theorem boundary. -/\ntheorem stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperCallStepInterface runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCall calleeName args =>\n rcases hstep\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperCallSurface] at hdirect\n · apply ih\n intro scope calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n List.mem_eraseDups_iff_local.mp h\n\nprivate theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCall calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact direct-helper-call list interface from head-step\nconstructors indexed only by helper callees that actually occur in the current\nstatement list. This matches the `helperCallNames`-based rank inventory carried\nby `SupportedBodyHelperInterface`, avoiding arbitrary-name quantification at the\nfunction theorem boundary. -/\ntheorem stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperCallStepInterface runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCall calleeName args =>\n rcases hstep\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperCallSurface] at hdirect\n · apply ih\n intro scope calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -354,11 +354,17 @@\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n \n+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n+\n private theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n+ {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n+ List.mem_eraseDups_iff_local.mpr h\n \n private theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n+ {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n+ List.mem_eraseDups_iff_local.mp h\n \n private theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21369,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_16"},"challenge_id":{"kind":"string","value":"b78fb7a5bef50c60"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":16,"string":"16"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_of_mem_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mpr h","n_chars":37,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2},{"theorem_name":"List.mem_of_mem_eraseDups_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mp h","n_chars":36,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_of_mem_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mpr h\",\n \"n_chars\": 37,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n },\n {\n \"theorem_name\": \"List.mem_of_mem_eraseDups_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mp h\",\n \"n_chars\": 36,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"List.mem_eraseDups_iff_local","text":"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n","fan_in":2,"n_lines":5,"n_chars":201,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_iff_local\",\n \"text\": \"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 201,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListDirectInternalHelperCallStepInterfaceWithInternals_of_internalCallSteps_of_helperCallNames","fan_in":0,"n_deps_direct":4,"n_deps_transitive":6,"n_lines":44,"n_chars":1872,"n_subproofs":1,"n_tactics":25,"cyclomatic":4,"n_automation":1,"n_rewrites":0,"n_structural":10,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"stmtListDirectInternalHelperCallStepInterfaceWithInternals_of_internalCallSteps_of_helperCallNames\",\n \"fan_in\": 0,\n \"n_deps_direct\": 4,\n \"n_deps_transitive\": 6,\n \"n_lines\": 44,\n \"n_chars\": 1872,\n \"n_subproofs\": 1,\n \"n_tactics\": 25,\n \"cyclomatic\": 4,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 10,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":6,"string":"6"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n\nprivate theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCall calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact `WithInternals` direct-helper-call list interface from\nhead-step constructors indexed only by helper callees in the current list. -/\ntheorem stmtListDirectInternalHelperCallStepInterfaceWithInternals_of_internalCallSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperCallStepInterfaceWithInternals\n runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCall calleeName args =>\n rcases hstep\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperCallSurface] at hdirect\n · apply ih\n intro scope calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n List.mem_eraseDups_iff_local.mp h\n\nprivate theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCall calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact `WithInternals` direct-helper-call list interface from\nhead-step constructors indexed only by helper callees in the current list. -/\ntheorem stmtListDirectInternalHelperCallStepInterfaceWithInternals_of_internalCallSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIRWithInternals\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperCallStepInterfaceWithInternals\n runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCall calleeName args =>\n rcases hstep\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperCallSurface] at hdirect\n · apply ih\n intro scope calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -354,11 +354,17 @@\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n \n+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n+\n private theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n+ {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n+ List.mem_eraseDups_iff_local.mpr h\n \n private theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n+ {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n+ List.mem_eraseDups_iff_local.mp h\n \n private theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21370,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_17"},"challenge_id":{"kind":"string","value":"99b3a9cabb76dc6e"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":17,"string":"17"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"List.mem_eraseDups_of_mem_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mpr h","n_chars":37,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2},{"theorem_name":"List.mem_of_mem_eraseDups_local","depth":1,"n_commands":0,"n_lines":2,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n List.mem_eraseDups_iff_local.mp h","n_chars":36,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"List.mem_eraseDups_of_mem_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mpr h\",\n \"n_chars\": 37,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n },\n {\n \"theorem_name\": \"List.mem_of_mem_eraseDups_local\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 2,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n List.mem_eraseDups_iff_local.mp h\",\n \"n_chars\": 36,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"List.mem_eraseDups_iff_local","text":"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n","fan_in":2,"n_lines":5,"n_chars":201,"n_subproofs":0,"n_tactics":1,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"List.mem_eraseDups_iff_local\",\n \"text\": \"private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 201,\n \"n_subproofs\": 0,\n \"n_tactics\": 1,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"stmtListDirectInternalHelperStepInterfaces_of_headStepCatalog","fan_in":0,"n_deps_direct":2,"n_deps_transitive":9,"n_lines":42,"n_chars":1358,"n_subproofs":0,"n_tactics":19,"cyclomatic":2,"n_automation":0,"n_rewrites":0,"n_structural":4,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"stmtListDirectInternalHelperStepInterfaces_of_headStepCatalog\",\n \"fan_in\": 0,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 9,\n \"n_lines\": 42,\n \"n_chars\": 1358,\n \"n_subproofs\": 0,\n \"n_tactics\": 19,\n \"cyclomatic\": 2,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":9,"string":"9"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n\nprivate theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCallAssign names calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCall calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact direct-helper-assign list interface from head-step\nconstructors indexed only by helper callees that actually occur in the current\nstatement list. This is the precise seam future helper-rank induction should\ntarget: it no longer needs to quantify over arbitrary helper names unrelated to\nthe body under proof. -/\ntheorem stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperAssignStepInterface runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCallAssign names calleeName args =>\n rcases hstep\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperAssignSurface] at hdirect\n · apply ih\n intro scope names calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (names := names) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\n/-- Assemble the exact direct-helper-call list interface from head-step\nconstructors indexed only by helper callees that actually occur in the current\nstatement list. This matches the `helperCallNames`-based rank inventory carried\nby `SupportedBodyHelperInterface`, avoiding arbitrary-name quantification at the\nfunction theorem boundary. -/\ntheorem stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperCallStepInterface runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCall calleeName args =>\n rcases hstep\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperCallSurface] at hdirect\n · apply ih\n intro scope calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\n/-- Assemble both exact direct-helper list interfaces from a single body-local\nhead-step catalog. This keeps the list recursion mechanical so future\nrank-decreasing helper proofs can focus on constructing one catalog object. -/\ntheorem stmtListDirectInternalHelperStepInterfaces_of_headStepCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {fn : FunctionSpec} :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn →\n StmtListDirectInternalHelperCallStepInterface\n runtimeContract\n spec\n fields\n scope\n fn.body ∧\n StmtListDirectInternalHelperAssignStepInterface\n runtimeContract\n spec\n fields\n scope\n fn.body := by\n intro hcatalog\n constructor\n · exact\n stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (stmts := fn.body)\n hcatalog.call\n · exact\n stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (stmts := fn.body)\n hcatalog.assign\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l = [] := List.eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero hlen)\n subst this\n exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | succ n ih =>\n match l with\n | [] => exact ⟨List.Pairwise.nil, fun _ => Iff.rfl⟩\n | x :: xs =>\n rw [List.eraseDups_cons]\n have hfilt_len : (xs.filter fun b => !b == x).length ≤ n := by\n have := List.length_filter_le (fun b => !b == x) xs\n simp [List.length_cons] at hlen\n omega\n have ⟨ihNd, ihMem⟩ := ih _ hfilt_len\n constructor\n · rw [List.nodup_cons]\n constructor\n · intro h\n have hmf := (ihMem x).mp h\n rw [List.mem_filter] at hmf\n have := hmf.2\n simp at this\n · exact ihNd\n · intro a\n constructor\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · exact Or.inr (List.mem_filter.mp ((ihMem a).mp h)).1\n · intro h\n rw [List.mem_cons] at h ⊢\n rcases h with rfl | h\n · exact Or.inl rfl\n · by_cases heq : a == x\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n\nprivate theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\nprivate theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n List.mem_eraseDups_iff_local.mpr h\n\nprivate theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n List.mem_eraseDups_iff_local.mp h\n\nprivate theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCallAssign names calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {calleeName : String} {args : List Expr} {rest : List Stmt} :\n calleeName ∈\n (stmtListInternalHelperCallNames\n (Stmt.internalCall calleeName args :: rest)).eraseDups := by\n apply List.mem_eraseDups_of_mem_local\n simp [stmtListInternalHelperCallNames, stmtInternalHelperCallNames]\n\nprivate theorem mem_stmtListInternalHelperCallNames_cons_of_mem_tail\n {stmt : Stmt} {rest : List Stmt} {calleeName : String}\n (hrest : calleeName ∈ stmtListInternalHelperCallNames rest) :\n calleeName ∈ stmtListInternalHelperCallNames (stmt :: rest) := by\n simp [stmtListInternalHelperCallNames, hrest]\n\n/-- Assemble the exact direct-helper-assign list interface from head-step\nconstructors indexed only by helper callees that actually occur in the current\nstatement list. This is the precise seam future helper-rank induction should\ntarget: it no longer needs to quantify over arbitrary helper names unrelated to\nthe body under proof. -/\ntheorem stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperAssignStepInterface runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCallAssign names calleeName args =>\n rcases hstep\n (scope := scope)\n (names := names)\n (calleeName := calleeName)\n (args := args)\n internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperAssignSurface] at hdirect\n · apply ih\n intro scope names calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (names := names) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\n/-- Assemble the exact direct-helper-call list interface from head-step\nconstructors indexed only by helper callees that actually occur in the current\nstatement list. This matches the `helperCallNames`-based rank inventory carried\nby `SupportedBodyHelperInterface`, avoiding arbitrary-name quantification at the\nfunction theorem boundary. -/\ntheorem stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {stmts : List Stmt}\n (hstep :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ (stmtListInternalHelperCallNames stmts).eraseDups →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract spec fields scope\n (Stmt.internalCall calleeName args)\n compiledIR) :\n StmtListDirectInternalHelperCallStepInterface runtimeContract spec fields scope stmts := by\n induction stmts generalizing scope with\n | nil =>\n exact .nil\n | cons stmt rest ih =>\n refine .cons ?_ ?_\n · intro hdirect\n cases stmt with\n | internalCall calleeName args =>\n rcases hstep\n (scope := scope)\n (calleeName := calleeName)\n (args := args)\n internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups with\n ⟨compiledIR, hcompiled⟩\n exact ⟨compiledIR, hcompiled⟩\n | _ =>\n simp [stmtTouchesDirectInternalHelperCallSurface] at hdirect\n · apply ih\n intro scope calleeName args hmem\n have hrest : calleeName ∈ stmtListInternalHelperCallNames rest :=\n List.mem_of_mem_eraseDups_local hmem\n exact hstep (scope := scope) (calleeName := calleeName) (args := args)\n (List.mem_eraseDups_of_mem_local\n (mem_stmtListInternalHelperCallNames_cons_of_mem_tail hrest))\n\n/-- Assemble both exact direct-helper list interfaces from a single body-local\nhead-step catalog. This keeps the list recursion mechanical so future\nrank-decreasing helper proofs can focus on constructing one catalog object. -/\ntheorem stmtListDirectInternalHelperStepInterfaces_of_headStepCatalog\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {fn : FunctionSpec} :\n DirectInternalHelperHeadStepCatalog runtimeContract spec fields fn →\n StmtListDirectInternalHelperCallStepInterface\n runtimeContract\n spec\n fields\n scope\n fn.body ∧\n StmtListDirectInternalHelperAssignStepInterface\n runtimeContract\n spec\n fields\n scope\n fn.body := by\n intro hcatalog\n constructor\n · exact\n stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (stmts := fn.body)\n hcatalog.call\n · exact\n stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames\n (runtimeContract := runtimeContract)\n (spec := spec)\n (fields := fields)\n (scope := scope)\n (stmts := fn.body)\n hcatalog.assign\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -354,11 +354,17 @@\n · exact Or.inl (beq_iff_eq.mp heq)\n · exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))\n \n+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n+ (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n+\n private theorem List.mem_eraseDups_of_mem_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups := sorry\n+ {a : α} {l : List α} (h : a ∈ l) : a ∈ l.eraseDups :=\n+ List.mem_eraseDups_iff_local.mpr h\n \n private theorem List.mem_of_mem_eraseDups_local [BEq α] [LawfulBEq α]\n- {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l := sorry\n+ {a : α} {l : List α} (h : a ∈ l.eraseDups) : a ∈ l :=\n+ List.mem_eraseDups_iff_local.mp h\n \n private theorem internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups\n {names : List String} {calleeName : String} {args : List Expr} {rest : List Stmt} :\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21371,"cells":{"task_id":{"kind":"string","value":"ablate_cdb08728ad51_18"},"challenge_id":{"kind":"string","value":"19c614555363a7ab"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean"},"theory":{"kind":"string","value":"Calls"},"variant":{"kind":"number","value":18,"string":"18"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":24,"string":"24"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"execIRStmtsWithInternals_of_internalCall_compiledHelperWitness","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hcalleeName : compiledHelper.sourceWitness.callee.name = calleeName :=\n compiledHelper.sourceWitness.nameEq\n have hfindSome :\n (findInternalFunction? runtimeContract\n (CompilationModel.internalFunctionYulName calleeName)).isSome = true :=\n by\n simpa [hcalleeName] using\n (findInternalFunction?_of_compileInternalFunction_mem\n compiledHelper.compileOk\n compiledHelper.presentInRuntime)\n cases hfind : findInternalFunction? runtimeContract\n (CompilationModel.internalFunctionYulName calleeName) with\n | none =>\n simp [hfind] at hfindSome\n | some helper =>\n rcases\n execIRStmtsWithInternals_of_internalCall_compile\n (fields := fields)\n (scope := scope)\n (functionName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n runtimeContract\n irFuel\n state\n helper\n argVals\n state'\n hcompile\n hfind\n argExprs\n hargCompile\n hargs\n (internalFunctionYulName_ne_stop calleeName)\n (internalFunctionYulName_ne_sstore calleeName)\n (internalFunctionYulName_ne_mstore calleeName)\n (internalFunctionYulName_ne_revert calleeName)\n (internalFunctionYulName_ne_return calleeName) with\n ⟨hshape, hexec⟩\n refine ⟨helper, ?_⟩\n exact ⟨hshape, ⟨rfl, hexec⟩⟩","n_chars":1489,"n_subproofs":2,"n_tactics":42,"cyclomatic":3,"n_automation":3,"n_rewrites":0,"n_structural":4,"automation_only":false,"max_nesting":12}],"string":"[\n {\n \"theorem_name\": \"execIRStmtsWithInternals_of_internalCall_compiledHelperWitness\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hcalleeName : compiledHelper.sourceWitness.callee.name = calleeName :=\\n compiledHelper.sourceWitness.nameEq\\n have hfindSome :\\n (findInternalFunction? runtimeContract\\n (CompilationModel.internalFunctionYulName calleeName)).isSome = true :=\\n by\\n simpa [hcalleeName] using\\n (findInternalFunction?_of_compileInternalFunction_mem\\n compiledHelper.compileOk\\n compiledHelper.presentInRuntime)\\n cases hfind : findInternalFunction? runtimeContract\\n (CompilationModel.internalFunctionYulName calleeName) with\\n | none =>\\n simp [hfind] at hfindSome\\n | some helper =>\\n rcases\\n execIRStmtsWithInternals_of_internalCall_compile\\n (fields := fields)\\n (scope := scope)\\n (functionName := calleeName)\\n (args := args)\\n (compiledIR := compiledIR)\\n runtimeContract\\n irFuel\\n state\\n helper\\n argVals\\n state'\\n hcompile\\n hfind\\n argExprs\\n hargCompile\\n hargs\\n (internalFunctionYulName_ne_stop calleeName)\\n (internalFunctionYulName_ne_sstore calleeName)\\n (internalFunctionYulName_ne_mstore calleeName)\\n (internalFunctionYulName_ne_revert calleeName)\\n (internalFunctionYulName_ne_return calleeName) with\\n ⟨hshape, hexec⟩\\n refine ⟨helper, ?_⟩\\n exact ⟨hshape, ⟨rfl, hexec⟩⟩\",\n \"n_chars\": 1489,\n \"n_subproofs\": 2,\n \"n_tactics\": 42,\n \"cyclomatic\": 3,\n \"n_automation\": 3,\n \"n_rewrites\": 0,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 12\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"internalFunctionYulName_ne_stop","text":"private theorem internalFunctionYulName_ne_stop\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"stop\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 's' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 's' := by decide\n exact hcontra h.2\n\n","fan_in":1,"n_lines":15,"n_chars":561,"n_subproofs":3,"n_tactics":11,"cyclomatic":2,"n_automation":3,"n_rewrites":0,"n_structural":4,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"internalFunctionYulName_ne_stop\",\n \"text\": \"private theorem internalFunctionYulName_ne_stop\\n (calleeName : String) :\\n CompilationModel.internalFunctionYulName calleeName ≠ \\\"stop\\\" := by\\n intro hEq\\n have hHead := congrArg (fun s => s.toList.head?) hEq\\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\\n cases hHead with\\n | inl h =>\\n have hcontra : (toString \\\"\\\").data.head? ≠ some 's' := by decide\\n exact hcontra h\\n | inr h =>\\n have hcontra : (toString \\\"internal_\\\").data.head? ≠ some 's' := by decide\\n exact hcontra h.2\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 15,\n \"n_chars\": 561,\n \"n_subproofs\": 3,\n \"n_tactics\": 11,\n \"cyclomatic\": 2,\n \"n_automation\": 3,\n \"n_rewrites\": 0,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"execIRStmtsWithInternals_of_internalCall_compiledHelperWitness","fan_in":0,"n_deps_direct":5,"n_deps_transitive":5,"n_lines":80,"n_chars":3196,"n_subproofs":2,"n_tactics":42,"cyclomatic":3,"n_automation":3,"n_rewrites":0,"n_structural":4,"automation_only":false,"max_nesting":12}],"string":"[\n {\n \"name\": \"execIRStmtsWithInternals_of_internalCall_compiledHelperWitness\",\n \"fan_in\": 0,\n \"n_deps_direct\": 5,\n \"n_deps_transitive\": 5,\n \"n_lines\": 80,\n \"n_chars\": 3196,\n \"n_subproofs\": 2,\n \"n_tactics\": 42,\n \"cyclomatic\": 3,\n \"n_automation\": 3,\n \"n_rewrites\": 0,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 12\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":5,"string":"5"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem internalFunctionYulName_ne_sstore\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"sstore\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 's' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 's' := by decide\n exact hcontra h.2\n\nprivate theorem internalFunctionYulName_ne_mstore\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"mstore\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 'm' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 'm' := by decide\n exact hcontra h.2\n\nprivate theorem internalFunctionYulName_ne_revert\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"revert\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 'r' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 'r' := by decide\n exact hcontra h.2\n\nprivate theorem internalFunctionYulName_ne_return\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"return\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 'r' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 'r' := by decide\n exact hcontra h.2\n\n/-- Runtime-helper-table packaged version of\n`execIRStmtsWithInternals_of_internalCall_compile`: the caller no longer threads\nraw helper lookup or builtin-name side conditions by hand. -/\ntheorem execIRStmtsWithInternals_of_internalCall_compiledHelperWitness\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String}\n {args : List Expr}\n {compiledIR : List YulStmt}\n (compiledHelper :\n SupportedCompiledInternalHelperWitness spec runtimeContract calleeName)\n (state : IRState)\n (irFuel : Nat)\n {argVals : List Nat}\n {state' : IRState}\n (hcompile :\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (argExprs : List YulExpr)\n (hargCompile :\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n (hargs :\n evalIRExprsWithInternals runtimeContract (irFuel + 1) state argExprs =\n .values argVals state') :\n ∃ helper,\n compiledIR = [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs)] ∧\n findInternalFunction? runtimeContract\n (CompilationModel.internalFunctionYulName calleeName) = some helper ∧\n execIRStmtsWithInternals runtimeContract (irFuel + 3) state compiledIR =\n match execIRInternalFunctionWithInternals runtimeContract irFuel state' helper argVals with\n | .values _ state'' => .continue state''\n | .stop state'' => .stop state''\n | .return value' state'' => .return value' state''\n | .revert state'' => .revert state'' := by\n have hcalleeName : compiledHelper.sourceWitness.callee.name = calleeName :=\n compiledHelper.sourceWitness.nameEq\n have hfindSome :\n (findInternalFunction? runtimeContract\n (CompilationModel.internalFunctionYulName calleeName)).isSome = true :=\n by\n simpa [hcalleeName] using\n (findInternalFunction?_of_compileInternalFunction_mem\n compiledHelper.compileOk\n compiledHelper.presentInRuntime)\n cases hfind : findInternalFunction? runtimeContract\n (CompilationModel.internalFunctionYulName calleeName) with\n | none =>\n simp [hfind] at hfindSome\n | some helper => sorry\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.GenericInduction.Core\n\nset_option linter.unnecessarySeqFocus false\nset_option linter.unnecessarySimpa false\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Yul\n\n/-- Exact Tier 4 head-step proof object for a function body's direct internal\nhelper surface. Future helper-rank induction should construct this single\ncatalog once, then reuse the mechanical list-interface assembly theorems\ndownstream. -/\nstructure DirectInternalHelperHeadStepCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCall calleeName args)\n compiledIR\n assign :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompiledStmtStepWithHelpersAndHelperIR\n runtimeContract\n spec\n fields\n scope\n (Stmt.internalCallAssign names calleeName args)\n compiledIR\n\n/-- Mid-level Tier 4 seam: future rank induction can package direct-helper\nsingletons here by proving compilation succeeds for the head and that the exact\nsingleton IR execution matches the source helper-aware step. The mechanical\n`CompiledStmtStepWithHelpersAndHelperIR` construction into\n`DirectInternalHelperHeadStepCatalog` is then shared. -/\nstructure DirectInternalHelperCallHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperAssignHeadStepBridge\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct call bridge. This is the direct-call counterpart\nof `DirectInternalHelperCallHeadStepBridge`, but it records the exact\n`compileStmt ... spec.functions` shape and the corresponding\n`compileInternalCallArgs ... spec.functions` argument compilation. -/\nstructure DirectInternalHelperCallHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCall calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Spec-functions-aware direct helper-return binding bridge. -/\nstructure DirectInternalHelperAssignHeadStepBridgeWithInternals\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (calleeName : String) : Prop where\n compile :\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR\n bridge :\n ∀ {scope : List String} {names : List String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n CompilationModel.compileStmt fields spec.events spec.errors .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) spec.functions = Except.ok compiledIR →\n CompilationModel.compileInternalCallArgs fields .calldata spec.functions\n calleeName args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\nstructure DirectInternalHelperHeadStepBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n callCompile :\n ∀ {scope : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n callBridge :\n ∀ {scope : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCall calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCall calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.exprStmt (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n assignCompile :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr},\n calleeName ∈ helperCallNames fn →\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n assignBridge :\n ∀ {scope : List String} {names : List String} {calleeName : String} {args : List Expr}\n {compiledIR : List YulStmt} {argExprs : List YulExpr},\n calleeName ∈ helperCallNames fn →\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR →\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs →\n ∀ (runtime : SourceSemantics.RuntimeState)\n (state : IRState)\n (helperFuel : Nat)\n (irFuel : Nat),\n 0 < helperFuel →\n FunctionBody.bindingsExactlyMatchIRVarsOnScope scope runtime.bindings state →\n FunctionBody.scopeNamesPresent scope runtime.bindings →\n FunctionBody.bindingsBounded runtime.bindings →\n FunctionBody.runtimeStateMatchesIR fields runtime state →\n stmtStepMatchesIRExecWithInternals fields\n (stmtNextScope scope (Stmt.internalCallAssign names calleeName args))\n (SourceSemantics.execStmtWithHelpers spec fields helperFuel runtime\n (Stmt.internalCallAssign names calleeName args))\n (execIRStmtsWithInternals runtimeContract (irFuel + 3) state\n [YulStmt.letMany names (YulExpr.call\n (CompilationModel.internalFunctionYulName calleeName) argExprs)])\n\n/-- Callee-local Tier 4 bridge inventory. This matches\n`SupportedBodyHelperInterface.calleeRanksDecrease` directly: future rank\ninduction can construct one reusable bridge object per referenced helper callee,\nand the body-level head-step bridge catalog is assembled mechanically. -/\nstructure DirectInternalHelperPerCalleeBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperCallHeadStepBridge runtimeContract spec fields calleeName\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Assign-only half of the callee-local Tier 4 bridge inventory. This isolates\nthe roadmap's current blocker, namely helper-return-binding steps, while the\nvoid-call half remains mechanically vacuous under the current fragment. -/\nstructure DirectInternalHelperPerCalleeAssignBridgeCatalog\n (runtimeContract : IRContract)\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName\n\n/-- Split compile-side Tier 4 inventory. This isolates the purely compilation\nobligations from the semantic bridge obligations so future fragment widening can\ndischarge compile success generically once direct helper calls are admitted into\nthe supported statement witness. -/\nstructure DirectInternalHelperPerCalleeCallCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n call :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR\n\n/-- Assign-only half of the compile-side Tier 4 inventory. This isolates the\ncurrent fragment-widening blocker once direct helper return-binding calls are\nadmitted into the supported statement witness. -/\nstructure DirectInternalHelperPerCalleeAssignCompileCatalog\n (spec : CompilationModel)\n (fields : List Field)\n (fn : FunctionSpec) : Prop where\n assign :\n ∀ {calleeName : String},\n calleeName ∈ helperCallNames fn →\n ∀ {scope : List String} {names : List String} {args : List Expr},\n ∃ compiledIR,\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n\nprivate theorem internalFunctionYulName_ne_stop\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"stop\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 's' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 's' := by decide\n exact hcontra h.2\n\nprivate theorem internalFunctionYulName_ne_sstore\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"sstore\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 's' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 's' := by decide\n exact hcontra h.2\n\nprivate theorem internalFunctionYulName_ne_mstore\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"mstore\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 'm' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 'm' := by decide\n exact hcontra h.2\n\nprivate theorem internalFunctionYulName_ne_revert\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"revert\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 'r' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 'r' := by decide\n exact hcontra h.2\n\nprivate theorem internalFunctionYulName_ne_return\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"return\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n cases hHead with\n | inl h =>\n have hcontra : (toString \"\").data.head? ≠ some 'r' := by decide\n exact hcontra h\n | inr h =>\n have hcontra : (toString \"internal_\").data.head? ≠ some 'r' := by decide\n exact hcontra h.2\n\n/-- Runtime-helper-table packaged version of\n`execIRStmtsWithInternals_of_internalCall_compile`: the caller no longer threads\nraw helper lookup or builtin-name side conditions by hand. -/\ntheorem execIRStmtsWithInternals_of_internalCall_compiledHelperWitness\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String}\n {args : List Expr}\n {compiledIR : List YulStmt}\n (compiledHelper :\n SupportedCompiledInternalHelperWitness spec runtimeContract calleeName)\n (state : IRState)\n (irFuel : Nat)\n {argVals : List Nat}\n {state' : IRState}\n (hcompile :\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCall calleeName args) = Except.ok compiledIR)\n (argExprs : List YulExpr)\n (hargCompile :\n CompilationModel.compileExprList fields .calldata args = Except.ok argExprs)\n (hargs :\n evalIRExprsWithInternals runtimeContract (irFuel + 1) state argExprs =\n .values argVals state') :\n ∃ helper,\n compiledIR = [YulStmt.exprStmt\n (YulExpr.call (CompilationModel.internalFunctionYulName calleeName) argExprs)] ∧\n findInternalFunction? runtimeContract\n (CompilationModel.internalFunctionYulName calleeName) = some helper ∧\n execIRStmtsWithInternals runtimeContract (irFuel + 3) state compiledIR =\n match execIRInternalFunctionWithInternals runtimeContract irFuel state' helper argVals with\n | .values _ state'' => .continue state''\n | .stop state'' => .stop state''\n | .return value' state'' => .return value' state''\n | .revert state'' => .revert state'' := by\n have hcalleeName : compiledHelper.sourceWitness.callee.name = calleeName :=\n compiledHelper.sourceWitness.nameEq\n have hfindSome :\n (findInternalFunction? runtimeContract\n (CompilationModel.internalFunctionYulName calleeName)).isSome = true :=\n by\n simpa [hcalleeName] using\n (findInternalFunction?_of_compileInternalFunction_mem\n compiledHelper.compileOk\n compiledHelper.presentInRuntime)\n cases hfind : findInternalFunction? runtimeContract\n (CompilationModel.internalFunctionYulName calleeName) with\n | none =>\n simp [hfind] at hfindSome\n | some helper =>\n rcases\n execIRStmtsWithInternals_of_internalCall_compile\n (fields := fields)\n (scope := scope)\n (functionName := calleeName)\n (args := args)\n (compiledIR := compiledIR)\n runtimeContract\n irFuel\n state\n helper\n argVals\n state'\n hcompile\n hfind\n argExprs\n hargCompile\n hargs\n (internalFunctionYulName_ne_stop calleeName)\n (internalFunctionYulName_ne_sstore calleeName)\n (internalFunctionYulName_ne_mstore calleeName)\n (internalFunctionYulName_ne_revert calleeName)\n (internalFunctionYulName_ne_return calleeName) with\n ⟨hshape, hexec⟩\n refine ⟨helper, ?_⟩\n exact ⟨hshape, ⟨rfl, hexec⟩⟩\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -312,6 +312,20 @@\n CompilationModel.compileStmt fields [] [] .calldata [] false scope []\n (Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR\n \n+private theorem internalFunctionYulName_ne_stop\n+ (calleeName : String) :\n+ CompilationModel.internalFunctionYulName calleeName ≠ \"stop\" := by\n+ intro hEq\n+ have hHead := congrArg (fun s => s.toList.head?) hEq\n+ simp [CompilationModel.internalFunctionYulName, CompilationModel.internalFunctionPrefix] at hHead\n+ cases hHead with\n+ | inl h =>\n+ have hcontra : (toString \"\").data.head? ≠ some 's' := by decide\n+ exact hcontra h\n+ | inr h =>\n+ have hcontra : (toString \"internal_\").data.head? ≠ some 's' := by decide\n+ exact hcontra h.2\n+\n private theorem internalFunctionYulName_ne_sstore\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"sstore\" := by\n@@ -419,7 +433,33 @@\n (CompilationModel.internalFunctionYulName calleeName) with\n | none =>\n simp [hfind] at hfindSome\n- | some helper => sorry\n+ | some helper =>\n+ rcases\n+ execIRStmtsWithInternals_of_internalCall_compile\n+ (fields := fields)\n+ (scope := scope)\n+ (functionName := calleeName)\n+ (args := args)\n+ (compiledIR := compiledIR)\n+ runtimeContract\n+ irFuel\n+ state\n+ helper\n+ argVals\n+ state'\n+ hcompile\n+ hfind\n+ argExprs\n+ hargCompile\n+ hargs\n+ (internalFunctionYulName_ne_stop calleeName)\n+ (internalFunctionYulName_ne_sstore calleeName)\n+ (internalFunctionYulName_ne_mstore calleeName)\n+ (internalFunctionYulName_ne_revert calleeName)\n+ (internalFunctionYulName_ne_return calleeName) with\n+ ⟨hshape, hexec⟩\n+ refine ⟨helper, ?_⟩\n+ exact ⟨hshape, ⟨rfl, hexec⟩⟩\n \n end Compiler.Proofs.IRGeneration\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21372,"cells":{"task_id":{"kind":"string","value":"ablate_4b939bb4e6c3_0"},"challenge_id":{"kind":"string","value":"5cd6f2ec043f4cef"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/Core/Int256.lean"},"theory":{"kind":"string","value":"Int256"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":3,"string":"3"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"minValue_le","depth":1,"n_commands":0,"n_lines":7,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\n have hraw : value.word.val < modulus := value.word.isLt\n simp [toInt_of_ge_signBit hge, minValue, modulus_eq_two_mul_signBit]\n omega","n_chars":295,"n_subproofs":2,"n_tactics":7,"cyclomatic":1,"n_automation":3,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"minValue_le\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 7,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n by_cases h : value.word.val < signBit\\n · simp [toInt_of_lt_signBit h, minValue]\\n · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\\n have hraw : value.word.val < modulus := value.word.isLt\\n simp [toInt_of_ge_signBit hge, minValue, modulus_eq_two_mul_signBit]\\n omega\",\n \"n_chars\": 295,\n \"n_subproofs\": 2,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 3,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"modulus_eq_two_mul_signBit","text":"theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\n native_decide\n\n","fan_in":1,"n_lines":4,"n_chars":82,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"modulus_eq_two_mul_signBit\",\n \"text\": \"theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\\n native_decide\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 4,\n \"n_chars\": 82,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"minValue_le","fan_in":1,"n_deps_direct":3,"n_deps_transitive":3,"n_lines":9,"n_chars":365,"n_subproofs":2,"n_tactics":7,"cyclomatic":1,"n_automation":3,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"minValue_le\",\n \"fan_in\": 1,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 3,\n \"n_lines\": 9,\n \"n_chars\": 365,\n \"n_subproofs\": 2,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 3,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Verity.Core.Uint256\n\nnamespace Verity.Core\n\nstructure Int256 where\n word : Uint256\n deriving DecidableEq\n\nnamespace Int256\n\ndef modulus : Nat := Uint256.modulus\n\ndef signBit : Nat := 2 ^ 255\n\ndef minValue : Int := -Int.ofNat signBit\n\ndef maxValue : Int := Int.ofNat signBit - 1\n\ndef ofUint256 (value : Uint256) : Int256 := ⟨value⟩\n\ndef toUint256 (value : Int256) : Uint256 := value.word\n\ndef toInt (value : Int256) : Int :=\n let raw : Nat := value.word\n if raw < signBit then\n Int.ofNat raw\n else\n Int.ofNat raw - Int.ofNat modulus\n\ndef ofInt (value : Int) : Int256 :=\n if value < 0 then\n ofUint256 <| Uint256.ofNat (modulus - (Int.natAbs value % modulus))\n else\n ofUint256 <| Uint256.ofNat value.toNat\n\ninstance : Inhabited Int256 := ⟨ofUint256 0⟩\ninstance : Repr Int256 := ⟨fun value _ => repr value.toInt⟩\ninstance : OfNat Int256 n := ⟨ofUint256 n⟩\ninstance : Coe Int256 Uint256 := ⟨toUint256⟩\ninstance : Coe Int256 Int := ⟨toInt⟩\ninstance : Coe Uint256 Int256 := ⟨ofUint256⟩\n\n@[simp] theorem toUint256_ofUint256 (value : Uint256) :\n toUint256 (ofUint256 value) = value := rfl\n\n@[simp] theorem ofUint256_toUint256 (value : Uint256) :\n (ofUint256 value : Int256).toUint256 = value := rfl\n\n@[simp] theorem ofInt_nonneg (value : Int) (h : ¬ value < 0) :\n (ofInt value).toUint256 = Uint256.ofNat value.toNat := by\n simp [ofInt, h]\n\n@[simp] theorem ofInt_neg (value : Int) (h : value < 0) :\n (ofInt value).toUint256 = Uint256.ofNat (modulus - (Int.natAbs value % modulus)) := by\n simp [ofInt, h]\n\n@[simp] theorem toInt_of_lt_signBit {value : Int256} (h : value.word.val < signBit) :\n (value : Int) = Int.ofNat value.word.val := by\n simp [Int256.toInt, h]\n\n@[simp] theorem toInt_of_ge_signBit {value : Int256} (h : signBit ≤ value.word.val) :\n (value : Int) = Int.ofNat value.word.val - Int.ofNat modulus := by\n have h' : ¬ value.word.val < signBit := Nat.not_lt_of_ge h\n simp [Int256.toInt, h']\n\ntheorem minValue_le (value : Int256) : minValue ≤ (value : Int) := by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n · sorry\n\n@[simp] theorem val_zero : ((0 : Int256) : Int) = 0 := by\n native_decide\n\n@[simp] theorem val_one : ((1 : Int256) : Int) = 1 := by\n native_decide\n\ndef add (a b : Int256) : Int256 := ofUint256 (a.word + b.word)\n\ndef sub (a b : Int256) : Int256 := ofUint256 (a.word - b.word)\n\ndef mul (a b : Int256) : Int256 := ofUint256 (a.word * b.word)\n\ndef neg (value : Int256) : Int256 := ofUint256 <| Uint256.ofNat (modulus - value.word.val)\n\n/-- Absolute value as `Nat`. Exposed for downstream bridge proofs. -/\ndef signedAbsNat (value : Int) : Nat := Int.natAbs value\n\ndef div (a b : Int256) : Int256 :=\n let lhs : Int := a\n let rhs : Int := b\n if rhs = 0 then\n 0\n else\n let quotient := signedAbsNat lhs / signedAbsNat rhs\n let sameSign := (lhs < 0) == (rhs < 0)\n if sameSign then\n ofInt (Int.ofNat quotient)\n else\n ofInt (-Int.ofNat quotient)\n\ndef mod (a b : Int256) : Int256 :=\n let lhs : Int := a\n let rhs : Int := b\n if rhs = 0 then\n 0\n else\n let remainder := signedAbsNat lhs % signedAbsNat rhs\n if lhs < 0 then\n ofInt (-Int.ofNat remainder)\n else\n ofInt (Int.ofNat remainder)\n\ndef sar (shift value : Int256) : Int256 :=\n let s := shift.word.val % modulus\n let v : Int := value\n if s ≥ 256 then\n if v < 0 then ofInt (-1) else 0\n else\n ofInt (Int.fdiv v (Int.ofNat (2 ^ s)))\n\ndef isNeg (value : Int256) : Bool :=\n signBit ≤ value.word.val\n\ndef isZero (value : Int256) : Bool :=\n value.word.val = 0\n\ninstance : LT Int256 := ⟨fun a b => (a : Int) < (b : Int)⟩\ninstance : LE Int256 := ⟨fun a b => (a : Int) ≤ (b : Int)⟩\ninstance (a b : Int256) : Decidable (a < b) := by\n change Decidable ((a : Int) < (b : Int))\n infer_instance\ninstance (a b : Int256) : Decidable (a ≤ b) := by\n change Decidable ((a : Int) ≤ (b : Int))\n infer_instance\n\n@[simp] theorem le_def (a b : Int256) : (a ≤ b) = ((a : Int) ≤ (b : Int)) := rfl\n@[simp] theorem lt_def (a b : Int256) : (a < b) = ((a : Int) < (b : Int)) := rfl\n\ninstance : HAdd Int256 Int256 Int256 := ⟨add⟩\ninstance : HSub Int256 Int256 Int256 := ⟨sub⟩\ninstance : HMul Int256 Int256 Int256 := ⟨mul⟩\ninstance : HDiv Int256 Int256 Int256 := ⟨div⟩\ninstance : HMod Int256 Int256 Int256 := ⟨mod⟩\ninstance : Add Int256 := ⟨add⟩\ninstance : Sub Int256 := ⟨sub⟩\ninstance : Mul Int256 := ⟨mul⟩\ninstance : Div Int256 := ⟨div⟩\ninstance : Mod Int256 := ⟨mod⟩\ninstance : Neg Int256 := ⟨neg⟩\n\n@[simp] theorem add_toUint256 (a b : Int256) :\n (a + b).toUint256 = a.toUint256 + b.toUint256 := rfl\n\n@[simp] theorem sub_toUint256 (a b : Int256) :\n (a - b).toUint256 = a.toUint256 - b.toUint256 := rfl\n\n@[simp] theorem mul_toUint256 (a b : Int256) :\n (a * b).toUint256 = a.toUint256 * b.toUint256 := rfl\n\n@[simp] theorem neg_toUint256 (value : Int256) :\n (-value).toUint256 = Uint256.ofNat (modulus - value.word.val) := rfl\n\n@[simp] theorem div_by_zero (value : Int256) : value / (0 : Int256) = 0 := by\n simp [HDiv.hDiv, Int256.div]\n\n@[simp] theorem mod_by_zero (value : Int256) : value % (0 : Int256) = 0 := by\n simp [HMod.hMod, Int256.mod]\n\n@[ext] theorem ext {a b : Int256} (h : a.word = b.word) : a = b := by\n cases a\n cases b\n cases h\n rfl\n\nsection Examples\n\nexample : (((Int256.ofUint256 (Uint256.ofNat (modulus - 1)) : Int256) : Int)) = -1 := by\n native_decide\n\nexample : (((Int256.ofUint256 (Uint256.ofNat signBit) : Int256) : Int)) = minValue := by\n native_decide\n\nexample : (Int256.ofInt (-1)).toUint256 = Uint256.ofNat (modulus - 1) := by\n native_decide\n\nexample : (Int256.ofInt minValue).toUint256 = Uint256.ofNat signBit := by\n native_decide\n\nexample : (-(Int256.ofInt minValue) : Int256) = Int256.ofInt minValue := by\n native_decide\n\nexample : (Int256.ofInt (-7) / Int256.ofInt 3 : Int256) = Int256.ofInt (-2) := by\n native_decide\n\nexample : (Int256.ofInt 7 / Int256.ofInt (-3) : Int256) = Int256.ofInt (-2) := by\n native_decide\n\nexample : (Int256.ofInt (-7) % Int256.ofInt 3 : Int256) = Int256.ofInt (-1) := by\n native_decide\n\nexample : (Int256.ofInt 7 % Int256.ofInt (-3) : Int256) = Int256.ofInt 1 := by\n native_decide\n\nexample : (Int256.ofInt (-7) / (0 : Int256) : Int256) = 0 := by\n native_decide\n\nexample : (Int256.ofInt (-7) % (0 : Int256) : Int256) = 0 := by\n native_decide\n\nexample : (Int256.ofInt minValue / Int256.ofInt (-1) : Int256) = Int256.ofInt minValue := by\n native_decide\n\nexample : (Int256.ofInt maxValue + 1 : Int256) = Int256.ofInt minValue := by\n native_decide\n\nend Examples\n\nend Int256\n\nend Verity.Core\n"},"solution_file_content":{"kind":"string","value":"import Verity.Core.Uint256\n\nnamespace Verity.Core\n\nstructure Int256 where\n word : Uint256\n deriving DecidableEq\n\nnamespace Int256\n\ndef modulus : Nat := Uint256.modulus\n\ndef signBit : Nat := 2 ^ 255\n\ndef minValue : Int := -Int.ofNat signBit\n\ndef maxValue : Int := Int.ofNat signBit - 1\n\ndef ofUint256 (value : Uint256) : Int256 := ⟨value⟩\n\ndef toUint256 (value : Int256) : Uint256 := value.word\n\ndef toInt (value : Int256) : Int :=\n let raw : Nat := value.word\n if raw < signBit then\n Int.ofNat raw\n else\n Int.ofNat raw - Int.ofNat modulus\n\ndef ofInt (value : Int) : Int256 :=\n if value < 0 then\n ofUint256 <| Uint256.ofNat (modulus - (Int.natAbs value % modulus))\n else\n ofUint256 <| Uint256.ofNat value.toNat\n\ninstance : Inhabited Int256 := ⟨ofUint256 0⟩\ninstance : Repr Int256 := ⟨fun value _ => repr value.toInt⟩\ninstance : OfNat Int256 n := ⟨ofUint256 n⟩\ninstance : Coe Int256 Uint256 := ⟨toUint256⟩\ninstance : Coe Int256 Int := ⟨toInt⟩\ninstance : Coe Uint256 Int256 := ⟨ofUint256⟩\n\n@[simp] theorem toUint256_ofUint256 (value : Uint256) :\n toUint256 (ofUint256 value) = value := rfl\n\n@[simp] theorem ofUint256_toUint256 (value : Uint256) :\n (ofUint256 value : Int256).toUint256 = value := rfl\n\n@[simp] theorem ofInt_nonneg (value : Int) (h : ¬ value < 0) :\n (ofInt value).toUint256 = Uint256.ofNat value.toNat := by\n simp [ofInt, h]\n\n@[simp] theorem ofInt_neg (value : Int) (h : value < 0) :\n (ofInt value).toUint256 = Uint256.ofNat (modulus - (Int.natAbs value % modulus)) := by\n simp [ofInt, h]\n\n@[simp] theorem toInt_of_lt_signBit {value : Int256} (h : value.word.val < signBit) :\n (value : Int) = Int.ofNat value.word.val := by\n simp [Int256.toInt, h]\n\n@[simp] theorem toInt_of_ge_signBit {value : Int256} (h : signBit ≤ value.word.val) :\n (value : Int) = Int.ofNat value.word.val - Int.ofNat modulus := by\n have h' : ¬ value.word.val < signBit := Nat.not_lt_of_ge h\n simp [Int256.toInt, h']\n\ntheorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\n native_decide\n\ntheorem minValue_le (value : Int256) : minValue ≤ (value : Int) := by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\n have hraw : value.word.val < modulus := value.word.isLt\n simp [toInt_of_ge_signBit hge, minValue, modulus_eq_two_mul_signBit]\n omega\n\n@[simp] theorem val_zero : ((0 : Int256) : Int) = 0 := by\n native_decide\n\n@[simp] theorem val_one : ((1 : Int256) : Int) = 1 := by\n native_decide\n\ndef add (a b : Int256) : Int256 := ofUint256 (a.word + b.word)\n\ndef sub (a b : Int256) : Int256 := ofUint256 (a.word - b.word)\n\ndef mul (a b : Int256) : Int256 := ofUint256 (a.word * b.word)\n\ndef neg (value : Int256) : Int256 := ofUint256 <| Uint256.ofNat (modulus - value.word.val)\n\n/-- Absolute value as `Nat`. Exposed for downstream bridge proofs. -/\ndef signedAbsNat (value : Int) : Nat := Int.natAbs value\n\ndef div (a b : Int256) : Int256 :=\n let lhs : Int := a\n let rhs : Int := b\n if rhs = 0 then\n 0\n else\n let quotient := signedAbsNat lhs / signedAbsNat rhs\n let sameSign := (lhs < 0) == (rhs < 0)\n if sameSign then\n ofInt (Int.ofNat quotient)\n else\n ofInt (-Int.ofNat quotient)\n\ndef mod (a b : Int256) : Int256 :=\n let lhs : Int := a\n let rhs : Int := b\n if rhs = 0 then\n 0\n else\n let remainder := signedAbsNat lhs % signedAbsNat rhs\n if lhs < 0 then\n ofInt (-Int.ofNat remainder)\n else\n ofInt (Int.ofNat remainder)\n\ndef sar (shift value : Int256) : Int256 :=\n let s := shift.word.val % modulus\n let v : Int := value\n if s ≥ 256 then\n if v < 0 then ofInt (-1) else 0\n else\n ofInt (Int.fdiv v (Int.ofNat (2 ^ s)))\n\ndef isNeg (value : Int256) : Bool :=\n signBit ≤ value.word.val\n\ndef isZero (value : Int256) : Bool :=\n value.word.val = 0\n\ninstance : LT Int256 := ⟨fun a b => (a : Int) < (b : Int)⟩\ninstance : LE Int256 := ⟨fun a b => (a : Int) ≤ (b : Int)⟩\ninstance (a b : Int256) : Decidable (a < b) := by\n change Decidable ((a : Int) < (b : Int))\n infer_instance\ninstance (a b : Int256) : Decidable (a ≤ b) := by\n change Decidable ((a : Int) ≤ (b : Int))\n infer_instance\n\n@[simp] theorem le_def (a b : Int256) : (a ≤ b) = ((a : Int) ≤ (b : Int)) := rfl\n@[simp] theorem lt_def (a b : Int256) : (a < b) = ((a : Int) < (b : Int)) := rfl\n\ninstance : HAdd Int256 Int256 Int256 := ⟨add⟩\ninstance : HSub Int256 Int256 Int256 := ⟨sub⟩\ninstance : HMul Int256 Int256 Int256 := ⟨mul⟩\ninstance : HDiv Int256 Int256 Int256 := ⟨div⟩\ninstance : HMod Int256 Int256 Int256 := ⟨mod⟩\ninstance : Add Int256 := ⟨add⟩\ninstance : Sub Int256 := ⟨sub⟩\ninstance : Mul Int256 := ⟨mul⟩\ninstance : Div Int256 := ⟨div⟩\ninstance : Mod Int256 := ⟨mod⟩\ninstance : Neg Int256 := ⟨neg⟩\n\n@[simp] theorem add_toUint256 (a b : Int256) :\n (a + b).toUint256 = a.toUint256 + b.toUint256 := rfl\n\n@[simp] theorem sub_toUint256 (a b : Int256) :\n (a - b).toUint256 = a.toUint256 - b.toUint256 := rfl\n\n@[simp] theorem mul_toUint256 (a b : Int256) :\n (a * b).toUint256 = a.toUint256 * b.toUint256 := rfl\n\n@[simp] theorem neg_toUint256 (value : Int256) :\n (-value).toUint256 = Uint256.ofNat (modulus - value.word.val) := rfl\n\n@[simp] theorem div_by_zero (value : Int256) : value / (0 : Int256) = 0 := by\n simp [HDiv.hDiv, Int256.div]\n\n@[simp] theorem mod_by_zero (value : Int256) : value % (0 : Int256) = 0 := by\n simp [HMod.hMod, Int256.mod]\n\n@[ext] theorem ext {a b : Int256} (h : a.word = b.word) : a = b := by\n cases a\n cases b\n cases h\n rfl\n\nsection Examples\n\nexample : (((Int256.ofUint256 (Uint256.ofNat (modulus - 1)) : Int256) : Int)) = -1 := by\n native_decide\n\nexample : (((Int256.ofUint256 (Uint256.ofNat signBit) : Int256) : Int)) = minValue := by\n native_decide\n\nexample : (Int256.ofInt (-1)).toUint256 = Uint256.ofNat (modulus - 1) := by\n native_decide\n\nexample : (Int256.ofInt minValue).toUint256 = Uint256.ofNat signBit := by\n native_decide\n\nexample : (-(Int256.ofInt minValue) : Int256) = Int256.ofInt minValue := by\n native_decide\n\nexample : (Int256.ofInt (-7) / Int256.ofInt 3 : Int256) = Int256.ofInt (-2) := by\n native_decide\n\nexample : (Int256.ofInt 7 / Int256.ofInt (-3) : Int256) = Int256.ofInt (-2) := by\n native_decide\n\nexample : (Int256.ofInt (-7) % Int256.ofInt 3 : Int256) = Int256.ofInt (-1) := by\n native_decide\n\nexample : (Int256.ofInt 7 % Int256.ofInt (-3) : Int256) = Int256.ofInt 1 := by\n native_decide\n\nexample : (Int256.ofInt (-7) / (0 : Int256) : Int256) = 0 := by\n native_decide\n\nexample : (Int256.ofInt (-7) % (0 : Int256) : Int256) = 0 := by\n native_decide\n\nexample : (Int256.ofInt minValue / Int256.ofInt (-1) : Int256) = Int256.ofInt minValue := by\n native_decide\n\nexample : (Int256.ofInt maxValue + 1 : Int256) = Int256.ofInt minValue := by\n native_decide\n\nend Examples\n\nend Int256\n\nend Verity.Core\n"},"solution_diff":{"kind":"string","value":"@@ -63,10 +63,16 @@\n have h' : ¬ value.word.val < signBit := Nat.not_lt_of_ge h\n simp [Int256.toInt, h']\n \n+theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\n+ native_decide\n+\n theorem minValue_le (value : Int256) : minValue ≤ (value : Int) := by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n- · sorry\n+ · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\n+ have hraw : value.word.val < modulus := value.word.isLt\n+ simp [toInt_of_ge_signBit hge, minValue, modulus_eq_two_mul_signBit]\n+ omega\n \n @[simp] theorem val_zero : ((0 : Int256) : Int) = 0 := by\n native_decide\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21373,"cells":{"task_id":{"kind":"string","value":"ablate_4b939bb4e6c3_1"},"challenge_id":{"kind":"string","value":"5a2d9e2b90ebbfae"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/Core/Int256.lean"},"theory":{"kind":"string","value":"Int256"},"variant":{"kind":"number","value":1,"string":"1"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":3,"string":"3"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"minValue_le","depth":1,"n_commands":0,"n_lines":7,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\n have hraw : value.word.val < modulus := value.word.isLt\n simp [toInt_of_ge_signBit hge, minValue, modulus_eq_two_mul_signBit]\n omega","n_chars":295,"n_subproofs":2,"n_tactics":7,"cyclomatic":1,"n_automation":3,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"minValue_le\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 7,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n by_cases h : value.word.val < signBit\\n · simp [toInt_of_lt_signBit h, minValue]\\n · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\\n have hraw : value.word.val < modulus := value.word.isLt\\n simp [toInt_of_ge_signBit hge, minValue, modulus_eq_two_mul_signBit]\\n omega\",\n \"n_chars\": 295,\n \"n_subproofs\": 2,\n \"n_tactics\": 7,\n \"cyclomatic\": 1,\n \"n_automation\": 3,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"modulus_eq_two_mul_signBit","text":"theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\n native_decide\n\n","fan_in":1,"n_lines":4,"n_chars":82,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"modulus_eq_two_mul_signBit\",\n \"text\": \"theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\\n native_decide\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 4,\n \"n_chars\": 82,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"toInt_in_range","fan_in":0,"n_deps_direct":2,"n_deps_transitive":5,"n_lines":4,"n_chars":158,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"toInt_in_range\",\n \"fan_in\": 0,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 5,\n \"n_lines\": 4,\n \"n_chars\": 158,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Verity.Core.Uint256\n\nnamespace Verity.Core\n\nstructure Int256 where\n word : Uint256\n deriving DecidableEq\n\nnamespace Int256\n\ndef modulus : Nat := Uint256.modulus\n\ndef signBit : Nat := 2 ^ 255\n\ndef minValue : Int := -Int.ofNat signBit\n\ndef maxValue : Int := Int.ofNat signBit - 1\n\ndef ofUint256 (value : Uint256) : Int256 := ⟨value⟩\n\ndef toUint256 (value : Int256) : Uint256 := value.word\n\ndef toInt (value : Int256) : Int :=\n let raw : Nat := value.word\n if raw < signBit then\n Int.ofNat raw\n else\n Int.ofNat raw - Int.ofNat modulus\n\ndef ofInt (value : Int) : Int256 :=\n if value < 0 then\n ofUint256 <| Uint256.ofNat (modulus - (Int.natAbs value % modulus))\n else\n ofUint256 <| Uint256.ofNat value.toNat\n\ninstance : Inhabited Int256 := ⟨ofUint256 0⟩\ninstance : Repr Int256 := ⟨fun value _ => repr value.toInt⟩\ninstance : OfNat Int256 n := ⟨ofUint256 n⟩\ninstance : Coe Int256 Uint256 := ⟨toUint256⟩\ninstance : Coe Int256 Int := ⟨toInt⟩\ninstance : Coe Uint256 Int256 := ⟨ofUint256⟩\n\n@[simp] theorem toUint256_ofUint256 (value : Uint256) :\n toUint256 (ofUint256 value) = value := rfl\n\n@[simp] theorem ofUint256_toUint256 (value : Uint256) :\n (ofUint256 value : Int256).toUint256 = value := rfl\n\n@[simp] theorem ofInt_nonneg (value : Int) (h : ¬ value < 0) :\n (ofInt value).toUint256 = Uint256.ofNat value.toNat := by\n simp [ofInt, h]\n\n@[simp] theorem ofInt_neg (value : Int) (h : value < 0) :\n (ofInt value).toUint256 = Uint256.ofNat (modulus - (Int.natAbs value % modulus)) := by\n simp [ofInt, h]\n\n@[simp] theorem toInt_of_lt_signBit {value : Int256} (h : value.word.val < signBit) :\n (value : Int) = Int.ofNat value.word.val := by\n simp [Int256.toInt, h]\n\n@[simp] theorem toInt_of_ge_signBit {value : Int256} (h : signBit ≤ value.word.val) :\n (value : Int) = Int.ofNat value.word.val - Int.ofNat modulus := by\n have h' : ¬ value.word.val < signBit := Nat.not_lt_of_ge h\n simp [Int256.toInt, h']\n\ntheorem minValue_le (value : Int256) : minValue ≤ (value : Int) := by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n · sorry\n\ntheorem le_maxValue (value : Int256) : (value : Int) ≤ maxValue := by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, maxValue]\n omega\n · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\n have hraw : value.word.val < modulus := value.word.isLt\n have hneg : (value : Int) ≤ -1 := by\n simp [toInt_of_ge_signBit hge]\n omega\n have hs : (0 : Int) ≤ Int.ofNat signBit := by\n simp\n have hmax : (-1 : Int) ≤ maxValue := by\n simp [maxValue]\n omega\n omega\n\ntheorem toInt_in_range (value : Int256) : minValue ≤ (value : Int) ∧ (value : Int) ≤ maxValue := by\n exact ⟨minValue_le value, le_maxValue value⟩\n\n@[simp] theorem val_zero : ((0 : Int256) : Int) = 0 := by\n native_decide\n\n@[simp] theorem val_one : ((1 : Int256) : Int) = 1 := by\n native_decide\n\ndef add (a b : Int256) : Int256 := ofUint256 (a.word + b.word)\n\ndef sub (a b : Int256) : Int256 := ofUint256 (a.word - b.word)\n\ndef mul (a b : Int256) : Int256 := ofUint256 (a.word * b.word)\n\ndef neg (value : Int256) : Int256 := ofUint256 <| Uint256.ofNat (modulus - value.word.val)\n\n/-- Absolute value as `Nat`. Exposed for downstream bridge proofs. -/\ndef signedAbsNat (value : Int) : Nat := Int.natAbs value\n\ndef div (a b : Int256) : Int256 :=\n let lhs : Int := a\n let rhs : Int := b\n if rhs = 0 then\n 0\n else\n let quotient := signedAbsNat lhs / signedAbsNat rhs\n let sameSign := (lhs < 0) == (rhs < 0)\n if sameSign then\n ofInt (Int.ofNat quotient)\n else\n ofInt (-Int.ofNat quotient)\n\ndef mod (a b : Int256) : Int256 :=\n let lhs : Int := a\n let rhs : Int := b\n if rhs = 0 then\n 0\n else\n let remainder := signedAbsNat lhs % signedAbsNat rhs\n if lhs < 0 then\n ofInt (-Int.ofNat remainder)\n else\n ofInt (Int.ofNat remainder)\n\ndef sar (shift value : Int256) : Int256 :=\n let s := shift.word.val % modulus\n let v : Int := value\n if s ≥ 256 then\n if v < 0 then ofInt (-1) else 0\n else\n ofInt (Int.fdiv v (Int.ofNat (2 ^ s)))\n\ndef isNeg (value : Int256) : Bool :=\n signBit ≤ value.word.val\n\ndef isZero (value : Int256) : Bool :=\n value.word.val = 0\n\ninstance : LT Int256 := ⟨fun a b => (a : Int) < (b : Int)⟩\ninstance : LE Int256 := ⟨fun a b => (a : Int) ≤ (b : Int)⟩\ninstance (a b : Int256) : Decidable (a < b) := by\n change Decidable ((a : Int) < (b : Int))\n infer_instance\ninstance (a b : Int256) : Decidable (a ≤ b) := by\n change Decidable ((a : Int) ≤ (b : Int))\n infer_instance\n\n@[simp] theorem le_def (a b : Int256) : (a ≤ b) = ((a : Int) ≤ (b : Int)) := rfl\n@[simp] theorem lt_def (a b : Int256) : (a < b) = ((a : Int) < (b : Int)) := rfl\n\ninstance : HAdd Int256 Int256 Int256 := ⟨add⟩\ninstance : HSub Int256 Int256 Int256 := ⟨sub⟩\ninstance : HMul Int256 Int256 Int256 := ⟨mul⟩\ninstance : HDiv Int256 Int256 Int256 := ⟨div⟩\ninstance : HMod Int256 Int256 Int256 := ⟨mod⟩\ninstance : Add Int256 := ⟨add⟩\ninstance : Sub Int256 := ⟨sub⟩\ninstance : Mul Int256 := ⟨mul⟩\ninstance : Div Int256 := ⟨div⟩\ninstance : Mod Int256 := ⟨mod⟩\ninstance : Neg Int256 := ⟨neg⟩\n\n@[simp] theorem add_toUint256 (a b : Int256) :\n (a + b).toUint256 = a.toUint256 + b.toUint256 := rfl\n\n@[simp] theorem sub_toUint256 (a b : Int256) :\n (a - b).toUint256 = a.toUint256 - b.toUint256 := rfl\n\n@[simp] theorem mul_toUint256 (a b : Int256) :\n (a * b).toUint256 = a.toUint256 * b.toUint256 := rfl\n\n@[simp] theorem neg_toUint256 (value : Int256) :\n (-value).toUint256 = Uint256.ofNat (modulus - value.word.val) := rfl\n\n@[simp] theorem div_by_zero (value : Int256) : value / (0 : Int256) = 0 := by\n simp [HDiv.hDiv, Int256.div]\n\n@[simp] theorem mod_by_zero (value : Int256) : value % (0 : Int256) = 0 := by\n simp [HMod.hMod, Int256.mod]\n\n@[ext] theorem ext {a b : Int256} (h : a.word = b.word) : a = b := by\n cases a\n cases b\n cases h\n rfl\n\nsection Examples\n\nexample : (((Int256.ofUint256 (Uint256.ofNat (modulus - 1)) : Int256) : Int)) = -1 := by\n native_decide\n\nexample : (((Int256.ofUint256 (Uint256.ofNat signBit) : Int256) : Int)) = minValue := by\n native_decide\n\nexample : (Int256.ofInt (-1)).toUint256 = Uint256.ofNat (modulus - 1) := by\n native_decide\n\nexample : (Int256.ofInt minValue).toUint256 = Uint256.ofNat signBit := by\n native_decide\n\nexample : (-(Int256.ofInt minValue) : Int256) = Int256.ofInt minValue := by\n native_decide\n\nexample : (Int256.ofInt (-7) / Int256.ofInt 3 : Int256) = Int256.ofInt (-2) := by\n native_decide\n\nexample : (Int256.ofInt 7 / Int256.ofInt (-3) : Int256) = Int256.ofInt (-2) := by\n native_decide\n\nexample : (Int256.ofInt (-7) % Int256.ofInt 3 : Int256) = Int256.ofInt (-1) := by\n native_decide\n\nexample : (Int256.ofInt 7 % Int256.ofInt (-3) : Int256) = Int256.ofInt 1 := by\n native_decide\n\nexample : (Int256.ofInt (-7) / (0 : Int256) : Int256) = 0 := by\n native_decide\n\nexample : (Int256.ofInt (-7) % (0 : Int256) : Int256) = 0 := by\n native_decide\n\nexample : (Int256.ofInt minValue / Int256.ofInt (-1) : Int256) = Int256.ofInt minValue := by\n native_decide\n\nexample : (Int256.ofInt maxValue + 1 : Int256) = Int256.ofInt minValue := by\n native_decide\n\nend Examples\n\nend Int256\n\nend Verity.Core\n"},"solution_file_content":{"kind":"string","value":"import Verity.Core.Uint256\n\nnamespace Verity.Core\n\nstructure Int256 where\n word : Uint256\n deriving DecidableEq\n\nnamespace Int256\n\ndef modulus : Nat := Uint256.modulus\n\ndef signBit : Nat := 2 ^ 255\n\ndef minValue : Int := -Int.ofNat signBit\n\ndef maxValue : Int := Int.ofNat signBit - 1\n\ndef ofUint256 (value : Uint256) : Int256 := ⟨value⟩\n\ndef toUint256 (value : Int256) : Uint256 := value.word\n\ndef toInt (value : Int256) : Int :=\n let raw : Nat := value.word\n if raw < signBit then\n Int.ofNat raw\n else\n Int.ofNat raw - Int.ofNat modulus\n\ndef ofInt (value : Int) : Int256 :=\n if value < 0 then\n ofUint256 <| Uint256.ofNat (modulus - (Int.natAbs value % modulus))\n else\n ofUint256 <| Uint256.ofNat value.toNat\n\ninstance : Inhabited Int256 := ⟨ofUint256 0⟩\ninstance : Repr Int256 := ⟨fun value _ => repr value.toInt⟩\ninstance : OfNat Int256 n := ⟨ofUint256 n⟩\ninstance : Coe Int256 Uint256 := ⟨toUint256⟩\ninstance : Coe Int256 Int := ⟨toInt⟩\ninstance : Coe Uint256 Int256 := ⟨ofUint256⟩\n\n@[simp] theorem toUint256_ofUint256 (value : Uint256) :\n toUint256 (ofUint256 value) = value := rfl\n\n@[simp] theorem ofUint256_toUint256 (value : Uint256) :\n (ofUint256 value : Int256).toUint256 = value := rfl\n\n@[simp] theorem ofInt_nonneg (value : Int) (h : ¬ value < 0) :\n (ofInt value).toUint256 = Uint256.ofNat value.toNat := by\n simp [ofInt, h]\n\n@[simp] theorem ofInt_neg (value : Int) (h : value < 0) :\n (ofInt value).toUint256 = Uint256.ofNat (modulus - (Int.natAbs value % modulus)) := by\n simp [ofInt, h]\n\n@[simp] theorem toInt_of_lt_signBit {value : Int256} (h : value.word.val < signBit) :\n (value : Int) = Int.ofNat value.word.val := by\n simp [Int256.toInt, h]\n\n@[simp] theorem toInt_of_ge_signBit {value : Int256} (h : signBit ≤ value.word.val) :\n (value : Int) = Int.ofNat value.word.val - Int.ofNat modulus := by\n have h' : ¬ value.word.val < signBit := Nat.not_lt_of_ge h\n simp [Int256.toInt, h']\n\ntheorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\n native_decide\n\ntheorem minValue_le (value : Int256) : minValue ≤ (value : Int) := by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\n have hraw : value.word.val < modulus := value.word.isLt\n simp [toInt_of_ge_signBit hge, minValue, modulus_eq_two_mul_signBit]\n omega\n\ntheorem le_maxValue (value : Int256) : (value : Int) ≤ maxValue := by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, maxValue]\n omega\n · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\n have hraw : value.word.val < modulus := value.word.isLt\n have hneg : (value : Int) ≤ -1 := by\n simp [toInt_of_ge_signBit hge]\n omega\n have hs : (0 : Int) ≤ Int.ofNat signBit := by\n simp\n have hmax : (-1 : Int) ≤ maxValue := by\n simp [maxValue]\n omega\n omega\n\ntheorem toInt_in_range (value : Int256) : minValue ≤ (value : Int) ∧ (value : Int) ≤ maxValue := by\n exact ⟨minValue_le value, le_maxValue value⟩\n\n@[simp] theorem val_zero : ((0 : Int256) : Int) = 0 := by\n native_decide\n\n@[simp] theorem val_one : ((1 : Int256) : Int) = 1 := by\n native_decide\n\ndef add (a b : Int256) : Int256 := ofUint256 (a.word + b.word)\n\ndef sub (a b : Int256) : Int256 := ofUint256 (a.word - b.word)\n\ndef mul (a b : Int256) : Int256 := ofUint256 (a.word * b.word)\n\ndef neg (value : Int256) : Int256 := ofUint256 <| Uint256.ofNat (modulus - value.word.val)\n\n/-- Absolute value as `Nat`. Exposed for downstream bridge proofs. -/\ndef signedAbsNat (value : Int) : Nat := Int.natAbs value\n\ndef div (a b : Int256) : Int256 :=\n let lhs : Int := a\n let rhs : Int := b\n if rhs = 0 then\n 0\n else\n let quotient := signedAbsNat lhs / signedAbsNat rhs\n let sameSign := (lhs < 0) == (rhs < 0)\n if sameSign then\n ofInt (Int.ofNat quotient)\n else\n ofInt (-Int.ofNat quotient)\n\ndef mod (a b : Int256) : Int256 :=\n let lhs : Int := a\n let rhs : Int := b\n if rhs = 0 then\n 0\n else\n let remainder := signedAbsNat lhs % signedAbsNat rhs\n if lhs < 0 then\n ofInt (-Int.ofNat remainder)\n else\n ofInt (Int.ofNat remainder)\n\ndef sar (shift value : Int256) : Int256 :=\n let s := shift.word.val % modulus\n let v : Int := value\n if s ≥ 256 then\n if v < 0 then ofInt (-1) else 0\n else\n ofInt (Int.fdiv v (Int.ofNat (2 ^ s)))\n\ndef isNeg (value : Int256) : Bool :=\n signBit ≤ value.word.val\n\ndef isZero (value : Int256) : Bool :=\n value.word.val = 0\n\ninstance : LT Int256 := ⟨fun a b => (a : Int) < (b : Int)⟩\ninstance : LE Int256 := ⟨fun a b => (a : Int) ≤ (b : Int)⟩\ninstance (a b : Int256) : Decidable (a < b) := by\n change Decidable ((a : Int) < (b : Int))\n infer_instance\ninstance (a b : Int256) : Decidable (a ≤ b) := by\n change Decidable ((a : Int) ≤ (b : Int))\n infer_instance\n\n@[simp] theorem le_def (a b : Int256) : (a ≤ b) = ((a : Int) ≤ (b : Int)) := rfl\n@[simp] theorem lt_def (a b : Int256) : (a < b) = ((a : Int) < (b : Int)) := rfl\n\ninstance : HAdd Int256 Int256 Int256 := ⟨add⟩\ninstance : HSub Int256 Int256 Int256 := ⟨sub⟩\ninstance : HMul Int256 Int256 Int256 := ⟨mul⟩\ninstance : HDiv Int256 Int256 Int256 := ⟨div⟩\ninstance : HMod Int256 Int256 Int256 := ⟨mod⟩\ninstance : Add Int256 := ⟨add⟩\ninstance : Sub Int256 := ⟨sub⟩\ninstance : Mul Int256 := ⟨mul⟩\ninstance : Div Int256 := ⟨div⟩\ninstance : Mod Int256 := ⟨mod⟩\ninstance : Neg Int256 := ⟨neg⟩\n\n@[simp] theorem add_toUint256 (a b : Int256) :\n (a + b).toUint256 = a.toUint256 + b.toUint256 := rfl\n\n@[simp] theorem sub_toUint256 (a b : Int256) :\n (a - b).toUint256 = a.toUint256 - b.toUint256 := rfl\n\n@[simp] theorem mul_toUint256 (a b : Int256) :\n (a * b).toUint256 = a.toUint256 * b.toUint256 := rfl\n\n@[simp] theorem neg_toUint256 (value : Int256) :\n (-value).toUint256 = Uint256.ofNat (modulus - value.word.val) := rfl\n\n@[simp] theorem div_by_zero (value : Int256) : value / (0 : Int256) = 0 := by\n simp [HDiv.hDiv, Int256.div]\n\n@[simp] theorem mod_by_zero (value : Int256) : value % (0 : Int256) = 0 := by\n simp [HMod.hMod, Int256.mod]\n\n@[ext] theorem ext {a b : Int256} (h : a.word = b.word) : a = b := by\n cases a\n cases b\n cases h\n rfl\n\nsection Examples\n\nexample : (((Int256.ofUint256 (Uint256.ofNat (modulus - 1)) : Int256) : Int)) = -1 := by\n native_decide\n\nexample : (((Int256.ofUint256 (Uint256.ofNat signBit) : Int256) : Int)) = minValue := by\n native_decide\n\nexample : (Int256.ofInt (-1)).toUint256 = Uint256.ofNat (modulus - 1) := by\n native_decide\n\nexample : (Int256.ofInt minValue).toUint256 = Uint256.ofNat signBit := by\n native_decide\n\nexample : (-(Int256.ofInt minValue) : Int256) = Int256.ofInt minValue := by\n native_decide\n\nexample : (Int256.ofInt (-7) / Int256.ofInt 3 : Int256) = Int256.ofInt (-2) := by\n native_decide\n\nexample : (Int256.ofInt 7 / Int256.ofInt (-3) : Int256) = Int256.ofInt (-2) := by\n native_decide\n\nexample : (Int256.ofInt (-7) % Int256.ofInt 3 : Int256) = Int256.ofInt (-1) := by\n native_decide\n\nexample : (Int256.ofInt 7 % Int256.ofInt (-3) : Int256) = Int256.ofInt 1 := by\n native_decide\n\nexample : (Int256.ofInt (-7) / (0 : Int256) : Int256) = 0 := by\n native_decide\n\nexample : (Int256.ofInt (-7) % (0 : Int256) : Int256) = 0 := by\n native_decide\n\nexample : (Int256.ofInt minValue / Int256.ofInt (-1) : Int256) = Int256.ofInt minValue := by\n native_decide\n\nexample : (Int256.ofInt maxValue + 1 : Int256) = Int256.ofInt minValue := by\n native_decide\n\nend Examples\n\nend Int256\n\nend Verity.Core\n"},"solution_diff":{"kind":"string","value":"@@ -63,10 +63,16 @@\n have h' : ¬ value.word.val < signBit := Nat.not_lt_of_ge h\n simp [Int256.toInt, h']\n \n+theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\n+ native_decide\n+\n theorem minValue_le (value : Int256) : minValue ≤ (value : Int) := by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n- · sorry\n+ · have hge : signBit ≤ value.word.val := Nat.le_of_not_lt h\n+ have hraw : value.word.val < modulus := value.word.isLt\n+ simp [toInt_of_ge_signBit hge, minValue, modulus_eq_two_mul_signBit]\n+ omega\n \n theorem le_maxValue (value : Int256) : (value : Int) ≤ maxValue := by\n by_cases h : value.word.val < signBit\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21374,"cells":{"task_id":{"kind":"string","value":"ablate_72489ced2f65_0"},"challenge_id":{"kind":"string","value":"02dba1d78c8e3651"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/YulGeneration/Backends/EvmYulLeanPureBuiltinLemmas.lean"},"theory":{"kind":"string","value":"EvmYulLeanPureBuiltinLemmas"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":6,"string":"6"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"slt_int256_eq_sltBool","depth":1,"n_commands":0,"n_lines":12,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n unfold EvmYul.UInt256.slt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sltBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt ha' hb']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega","n_chars":628,"n_subproofs":2,"n_tactics":14,"cyclomatic":3,"n_automation":7,"n_rewrites":3,"n_structural":0,"automation_only":false,"max_nesting":4},{"theorem_name":"sgt_int256_eq_sgtBool","depth":1,"n_commands":0,"n_lines":12,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n unfold EvmYul.UInt256.sgt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sgtBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt hb' ha']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega","n_chars":628,"n_subproofs":2,"n_tactics":14,"cyclomatic":3,"n_automation":7,"n_rewrites":3,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"slt_int256_eq_sltBool\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 12,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n unfold EvmYul.UInt256.slt\\n rw [toNat_fromBool]\\n unfold EvmYul.UInt256.sltBool\\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\\n simp only [uint256_lt_iff_nat_lt ha' hb']\\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\",\n \"n_chars\": 628,\n \"n_subproofs\": 2,\n \"n_tactics\": 14,\n \"cyclomatic\": 3,\n \"n_automation\": 7,\n \"n_rewrites\": 3,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n },\n {\n \"theorem_name\": \"sgt_int256_eq_sgtBool\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 12,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n unfold EvmYul.UInt256.sgt\\n rw [toNat_fromBool]\\n unfold EvmYul.UInt256.sgtBool\\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\\n simp only [uint256_lt_iff_nat_lt hb' ha']\\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\",\n \"n_chars\": 628,\n \"n_subproofs\": 2,\n \"n_tactics\": 14,\n \"cyclomatic\": 3,\n \"n_automation\": 7,\n \"n_rewrites\": 3,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"toNat_fromBool","text":"private theorem toNat_fromBool (b : Bool) :\n EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\n cases b <;> rfl\n\n","fan_in":2,"n_lines":5,"n_chars":134,"n_subproofs":0,"n_tactics":3,"cyclomatic":3,"n_automation":1,"n_rewrites":0,"n_structural":1,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"toNat_fromBool\",\n \"text\": \"private theorem toNat_fromBool (b : Bool) :\\n EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\\n cases b <;> rfl\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 134,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 3,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"slt_int256_eq_sltBool","fan_in":1,"n_deps_direct":9,"n_deps_transitive":3,"n_lines":22,"n_chars":1144,"n_subproofs":2,"n_tactics":14,"cyclomatic":3,"n_automation":7,"n_rewrites":3,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"slt_int256_eq_sltBool\",\n \"fan_in\": 1,\n \"n_deps_direct\": 9,\n \"n_deps_transitive\": 3,\n \"n_lines\": 22,\n \"n_chars\": 1144,\n \"n_subproofs\": 2,\n \"n_tactics\": 14,\n \"cyclomatic\": 3,\n \"n_automation\": 7,\n \"n_rewrites\": 3,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas\nimport Mathlib.Data.Nat.Bitwise\nimport Verity.Core.Int256\nimport Verity.Core.Uint256\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nprivate theorem uint256_size_eq_evmModulus :\n EvmYul.UInt256.size = Compiler.Constants.evmModulus := by\n decide\n\nprivate theorem word_lt_uint256_size (x : Nat) :\n x % EvmYul.UInt256.size < 2 ^ 256 := by\n simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_add_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"add\" [a, b] =\n some ((a + b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a + Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a + b) % EvmYul.UInt256.size)\n simp [Fin.val_add, Nat.add_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sub_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sub\" [a, b] =\n some ((Compiler.Constants.evmModulus + (a % Compiler.Constants.evmModulus) -\n (b % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a - Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)\n have hsub :\n EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size =\n EvmYul.UInt256.size - b % EvmYul.UInt256.size + a % EvmYul.UInt256.size := by\n have hb : b % EvmYul.UInt256.size ≤ EvmYul.UInt256.size := by\n exact Nat.le_of_lt (Nat.mod_lt _ (by simp [EvmYul.UInt256.size]))\n omega\n simp [Fin.sub_def, Nat.add_mod, hsub]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mul_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mul\" [a, b] =\n some ((a * b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a * Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a * b) % EvmYul.UInt256.size)\n simp [Fin.mul_def, Nat.mul_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_div_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"div\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) / (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a / Fin.ofNat EvmYul.UInt256.size b).val) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) / (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0 <;> simp [hb]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mod\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) % (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) % (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0\n · have hb0val : ((EvmYul.UInt256.ofNat b).val).val = 0 := by\n change b % EvmYul.UInt256.size = 0\n exact hb\n have hb0 : (EvmYul.UInt256.ofNat b).val = 0 := Fin.ext hb0val\n simp [EvmYul.UInt256.mod, EvmYul.UInt256.toNat, hb, hb0]\n · have hb0 : ¬ (EvmYul.UInt256.ofNat b).val = 0 := by\n intro h\n exact hb (congrArg Fin.val h)\n rw [show EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b) =\n ⟨(EvmYul.UInt256.ofNat a).val % (EvmYul.UInt256.ofNat b).val⟩ by\n simp [EvmYul.UInt256.mod, hb0]]\n simp [hb, EvmYul.UInt256.toNat]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_eq_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"eq\" [a, b] =\n some (if a % Compiler.Constants.evmModulus = b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_iszero_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"iszero\" [a] =\n some (if a % Compiler.Constants.evmModulus = 0 then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_lt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"lt\" [a, b] =\n some (if a % Compiler.Constants.evmModulus < b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_gt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"gt\" [a, b] =\n some (if b % Compiler.Constants.evmModulus < a % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\nprivate theorem uint256_lt_iff_nat_lt {a b : Nat}\n (ha : a < EvmYul.UInt256.size) (hb : b < EvmYul.UInt256.size) :\n ((⟨⟨a, ha⟩⟩ : EvmYul.UInt256) < ⟨⟨b, hb⟩⟩) ↔ (a < b) :=\n Iff.rfl\n\nprivate theorem slt_int256_eq_sltBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := sorry\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_slt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"slt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (slt_int256_eq_sltBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\nprivate theorem sgt_int256_eq_sgtBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := sorry\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sgt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sgt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (sgt_int256_eq_sgtBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sdiv_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sdiv\" [a, b] =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sdiv (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_div_toUint256_val_eq_uint256_sdiv\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_smod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"smod\" [a, b] =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.smod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_mod_toUint256_val_eq_uint256_smod\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sar_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"sar\" [shift, value] =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val := by\n have hs : shift % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt shift (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sar (EvmYul.UInt256.ofNat shift) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat shift =\n (⟨⟨shift % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hs⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_s :\n (shift % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n shift % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hs)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_s, hmod_v]\n exact (int256_sar_toUint256_val_eq_uint256_sar\n (shift % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hs hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_signextend_native (byteIdx value : Nat) :\n evalPureBuiltinViaEvmYulLean \"signextend\" [byteIdx, value] =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n have hb : byteIdx % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt byteIdx (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.signextend (EvmYul.UInt256.ofNat byteIdx) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val\n congr 1\n rw [show EvmYul.UInt256.ofNat byteIdx =\n (⟨⟨byteIdx % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_b :\n (byteIdx % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n byteIdx % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_b, hmod_v]\n exact (uint256_signextend_val_eq_uint256_signextend\n (byteIdx % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hb hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_and_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"and\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.and) (n := 256)\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt a (by decide : 0 < EvmYul.UInt256.size))\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt b (by decide : 0 < EvmYul.UInt256.size))\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_or_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"or\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.or) (n := 256)\n (word_lt_uint256_size a) (word_lt_uint256_size b)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_xor_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"xor\" [a, b] =\n some (Nat.xor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)) =\n some (a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size)\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)\n\nprivate theorem xor_all_ones_uint256_word (a : Nat) :\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n calc\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n ((BitVec.ofNat 256 a) ^^^ BitVec.allOnes 256).toNat := by\n simp [BitVec.toNat_xor, EvmYul.UInt256.size]\n _ = (~~~(BitVec.ofNat 256 a)).toNat := by\n rw [BitVec.xor_allOnes]\n _ = EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n simp [BitVec.toNat_not, EvmYul.UInt256.size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_not_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (Nat.xor (a % Compiler.Constants.evmModulus)\n (Compiler.Constants.evmModulus - 1)) := by\n rw [← uint256_size_eq_evmModulus]\n change evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some ((a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1))\n have hsub : evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n change evalPureBuiltinViaEvmYulLean \"sub\" [EvmYul.UInt256.size - 1, a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size))\n rw [evalPureBuiltinViaEvmYulLean_sub_native]\n rw [← uint256_size_eq_evmModulus]\n have hs : 0 < EvmYul.UInt256.size := by simp [EvmYul.UInt256.size]\n have ha : a % EvmYul.UInt256.size < EvmYul.UInt256.size := Nat.mod_lt _ hs\n have hlt : EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) < EvmYul.UInt256.size := by\n omega\n have hmod :\n ((EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size -\n a % EvmYul.UInt256.size) % EvmYul.UInt256.size) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n have hsizeMinusOneMod :\n (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size = EvmYul.UInt256.size - 1 := by\n exact Nat.mod_eq_of_lt (by omega)\n rw [hsizeMinusOneMod]\n have harr :\n EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) - a % EvmYul.UInt256.size =\n EvmYul.UInt256.size +\n (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n omega\n rw [harr, Nat.add_mod_left, Nat.mod_eq_of_lt hlt]\n exact congrArg some hmod\n rw [hsub]\n simp [xor_all_ones_uint256_word]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shl_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shl\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n ((value % Compiler.Constants.evmModulus) *\n 2 ^ (shift % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftLeft (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n ((value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs', Nat.shiftLeft_eq]\n change (value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size) %\n EvmYul.UInt256.size =\n value * 2 ^ (shift % EvmYul.UInt256.size) % EvmYul.UInt256.size\n rw [Nat.mul_mod, Nat.mul_mod]\n simp\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs']\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shr_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shr\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n (value % Compiler.Constants.evmModulus) /\n 2 ^ (shift % Compiler.Constants.evmModulus)\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n (value % EvmYul.UInt256.size) / 2 ^ (shift % EvmYul.UInt256.size)\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs', Nat.shiftRight_eq_div_pow]\n change value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size) =\n value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size)\n rfl\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs']\n\nprivate theorem nat_land_0xFF (n : Nat) : Nat.land n 255 = n % 256 := by\n rw [show (255 : Nat) = 2 ^ 8 - 1 from by omega]\n exact Nat.and_two_pow_sub_one_eq_mod n 8\n\nset_option maxHeartbeats 16000000 in\nprivate theorem evalPureBuiltinViaEvmYulLean_byte_normalized (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n (if index % EvmYul.UInt256.size > 31 then some 0\n else some ((value % EvmYul.UInt256.size /\n 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) % 256)) := by\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.byteAt (EvmYul.UInt256.ofNat index) (EvmYul.UInt256.ofNat value))) = _\n by_cases hgt : index % EvmYul.UInt256.size > 31\n · have hgt' : EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256) := by\n show (31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val\n show (31 : Nat) < index % EvmYul.UInt256.size\n exact hgt\n simp [hgt, EvmYul.UInt256.byteAt, hgt', EvmYul.UInt256.toNat]\n · have hle' : ¬(EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256)) := by\n show ¬((31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val)\n show ¬((31 : Nat) < index % EvmYul.UInt256.size)\n exact hgt\n have hshift_small : (31 - index % EvmYul.UInt256.size) * 8 < EvmYul.UInt256.size := by\n unfold EvmYul.UInt256.size; omega\n have hguard : ¬ 256 ≤ (EvmYul.UInt256.ofNat\n ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)).val := by\n change ¬ 256 ≤ ((31 - index % EvmYul.UInt256.size) * 8) % EvmYul.UInt256.size\n rw [Nat.mod_eq_of_lt hshift_small]; omega\n unfold EvmYul.UInt256.byteAt\n rw [if_neg hle']\n show some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.land\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value)\n (EvmYul.UInt256.ofNat ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)))\n ⟨255⟩)) = _\n unfold EvmYul.UInt256.shiftRight\n rw [if_neg hguard]\n simp only [hgt, ite_false, EvmYul.UInt256.land, EvmYul.UInt256.toNat,\n EvmYul.UInt256.ofNat, Id.run, Fin.land, Fin.shiftRight, Fin.ofNat,\n Nat.shiftRight_eq_div_pow]\n rw [Nat.mod_eq_of_lt hshift_small]\n rw [show (255 : Nat) % EvmYul.UInt256.size = 255 from by unfold EvmYul.UInt256.size; omega]\n have hdiv_lt :\n value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8) <\n EvmYul.UInt256.size :=\n Nat.lt_of_le_of_lt (Nat.div_le_self _ _)\n (Nat.mod_lt value (by unfold EvmYul.UInt256.size; omega))\n rw [Nat.mod_eq_of_lt hdiv_lt]\n rw [nat_land_0xFF]\n have hmod256_lt_size :\n (value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) %\n 256 < EvmYul.UInt256.size :=\n Nat.lt_trans (Nat.mod_lt _ (by omega)) (by unfold EvmYul.UInt256.size; omega)\n rw [Nat.mod_eq_of_lt hmod256_lt_size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_byte_native (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n some (Verity.Core.Uint256.byte\n (Verity.Core.Uint256.ofNat (index % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n rw [evalPureBuiltinViaEvmYulLean_byte_normalized]\n have hindexMod :\n index % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n index % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n have hvalueMod :\n value % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n value % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n rw [uint256_size_eq_evmModulus]\n simp [Verity.Core.Uint256.byte, hindexMod, hvalueMod]\n by_cases hgt : 31 < index % Compiler.Constants.evmModulus\n · simp [hgt]\n · simp [hgt, Nat.shiftRight_eq_div_pow]\n rw [show (255 : Nat) = 2 ^ 8 - 1 by omega]\n rw [Nat.and_two_pow_sub_one_eq_mod]\n rw [show (2 ^ 8 : Nat) = 256 by norm_num]\n have hlt :\n (value % Compiler.Constants.evmModulus /\n 2 ^ ((31 - index % Compiler.Constants.evmModulus) * 8)) %\n 256 < Verity.Core.Uint256.modulus :=\n Nat.lt_trans (Nat.mod_lt _ (by decide : 0 < 256))\n (by norm_num [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS])\n rw [Nat.mod_eq_of_lt hlt]\n\nend Compiler.Proofs.YulGeneration.Backends\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas\nimport Mathlib.Data.Nat.Bitwise\nimport Verity.Core.Int256\nimport Verity.Core.Uint256\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nprivate theorem uint256_size_eq_evmModulus :\n EvmYul.UInt256.size = Compiler.Constants.evmModulus := by\n decide\n\nprivate theorem word_lt_uint256_size (x : Nat) :\n x % EvmYul.UInt256.size < 2 ^ 256 := by\n simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_add_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"add\" [a, b] =\n some ((a + b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a + Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a + b) % EvmYul.UInt256.size)\n simp [Fin.val_add, Nat.add_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sub_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sub\" [a, b] =\n some ((Compiler.Constants.evmModulus + (a % Compiler.Constants.evmModulus) -\n (b % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a - Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)\n have hsub :\n EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size =\n EvmYul.UInt256.size - b % EvmYul.UInt256.size + a % EvmYul.UInt256.size := by\n have hb : b % EvmYul.UInt256.size ≤ EvmYul.UInt256.size := by\n exact Nat.le_of_lt (Nat.mod_lt _ (by simp [EvmYul.UInt256.size]))\n omega\n simp [Fin.sub_def, Nat.add_mod, hsub]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mul_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mul\" [a, b] =\n some ((a * b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a * Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a * b) % EvmYul.UInt256.size)\n simp [Fin.mul_def, Nat.mul_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_div_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"div\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) / (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a / Fin.ofNat EvmYul.UInt256.size b).val) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) / (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0 <;> simp [hb]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mod\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) % (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) % (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0\n · have hb0val : ((EvmYul.UInt256.ofNat b).val).val = 0 := by\n change b % EvmYul.UInt256.size = 0\n exact hb\n have hb0 : (EvmYul.UInt256.ofNat b).val = 0 := Fin.ext hb0val\n simp [EvmYul.UInt256.mod, EvmYul.UInt256.toNat, hb, hb0]\n · have hb0 : ¬ (EvmYul.UInt256.ofNat b).val = 0 := by\n intro h\n exact hb (congrArg Fin.val h)\n rw [show EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b) =\n ⟨(EvmYul.UInt256.ofNat a).val % (EvmYul.UInt256.ofNat b).val⟩ by\n simp [EvmYul.UInt256.mod, hb0]]\n simp [hb, EvmYul.UInt256.toNat]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_eq_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"eq\" [a, b] =\n some (if a % Compiler.Constants.evmModulus = b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_iszero_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"iszero\" [a] =\n some (if a % Compiler.Constants.evmModulus = 0 then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_lt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"lt\" [a, b] =\n some (if a % Compiler.Constants.evmModulus < b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_gt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"gt\" [a, b] =\n some (if b % Compiler.Constants.evmModulus < a % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\nprivate theorem toNat_fromBool (b : Bool) :\n EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\n cases b <;> rfl\n\nprivate theorem uint256_lt_iff_nat_lt {a b : Nat}\n (ha : a < EvmYul.UInt256.size) (hb : b < EvmYul.UInt256.size) :\n ((⟨⟨a, ha⟩⟩ : EvmYul.UInt256) < ⟨⟨b, hb⟩⟩) ↔ (a < b) :=\n Iff.rfl\n\nprivate theorem slt_int256_eq_sltBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.slt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sltBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt ha' hb']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_slt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"slt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (slt_int256_eq_sltBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\nprivate theorem sgt_int256_eq_sgtBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.sgt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sgtBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt hb' ha']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sgt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sgt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (sgt_int256_eq_sgtBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sdiv_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sdiv\" [a, b] =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sdiv (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_div_toUint256_val_eq_uint256_sdiv\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_smod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"smod\" [a, b] =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.smod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_mod_toUint256_val_eq_uint256_smod\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sar_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"sar\" [shift, value] =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val := by\n have hs : shift % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt shift (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sar (EvmYul.UInt256.ofNat shift) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat shift =\n (⟨⟨shift % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hs⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_s :\n (shift % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n shift % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hs)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_s, hmod_v]\n exact (int256_sar_toUint256_val_eq_uint256_sar\n (shift % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hs hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_signextend_native (byteIdx value : Nat) :\n evalPureBuiltinViaEvmYulLean \"signextend\" [byteIdx, value] =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n have hb : byteIdx % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt byteIdx (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.signextend (EvmYul.UInt256.ofNat byteIdx) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val\n congr 1\n rw [show EvmYul.UInt256.ofNat byteIdx =\n (⟨⟨byteIdx % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_b :\n (byteIdx % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n byteIdx % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_b, hmod_v]\n exact (uint256_signextend_val_eq_uint256_signextend\n (byteIdx % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hb hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_and_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"and\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.and) (n := 256)\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt a (by decide : 0 < EvmYul.UInt256.size))\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt b (by decide : 0 < EvmYul.UInt256.size))\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_or_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"or\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.or) (n := 256)\n (word_lt_uint256_size a) (word_lt_uint256_size b)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_xor_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"xor\" [a, b] =\n some (Nat.xor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)) =\n some (a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size)\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)\n\nprivate theorem xor_all_ones_uint256_word (a : Nat) :\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n calc\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n ((BitVec.ofNat 256 a) ^^^ BitVec.allOnes 256).toNat := by\n simp [BitVec.toNat_xor, EvmYul.UInt256.size]\n _ = (~~~(BitVec.ofNat 256 a)).toNat := by\n rw [BitVec.xor_allOnes]\n _ = EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n simp [BitVec.toNat_not, EvmYul.UInt256.size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_not_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (Nat.xor (a % Compiler.Constants.evmModulus)\n (Compiler.Constants.evmModulus - 1)) := by\n rw [← uint256_size_eq_evmModulus]\n change evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some ((a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1))\n have hsub : evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n change evalPureBuiltinViaEvmYulLean \"sub\" [EvmYul.UInt256.size - 1, a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size))\n rw [evalPureBuiltinViaEvmYulLean_sub_native]\n rw [← uint256_size_eq_evmModulus]\n have hs : 0 < EvmYul.UInt256.size := by simp [EvmYul.UInt256.size]\n have ha : a % EvmYul.UInt256.size < EvmYul.UInt256.size := Nat.mod_lt _ hs\n have hlt : EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) < EvmYul.UInt256.size := by\n omega\n have hmod :\n ((EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size -\n a % EvmYul.UInt256.size) % EvmYul.UInt256.size) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n have hsizeMinusOneMod :\n (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size = EvmYul.UInt256.size - 1 := by\n exact Nat.mod_eq_of_lt (by omega)\n rw [hsizeMinusOneMod]\n have harr :\n EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) - a % EvmYul.UInt256.size =\n EvmYul.UInt256.size +\n (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n omega\n rw [harr, Nat.add_mod_left, Nat.mod_eq_of_lt hlt]\n exact congrArg some hmod\n rw [hsub]\n simp [xor_all_ones_uint256_word]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shl_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shl\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n ((value % Compiler.Constants.evmModulus) *\n 2 ^ (shift % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftLeft (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n ((value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs', Nat.shiftLeft_eq]\n change (value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size) %\n EvmYul.UInt256.size =\n value * 2 ^ (shift % EvmYul.UInt256.size) % EvmYul.UInt256.size\n rw [Nat.mul_mod, Nat.mul_mod]\n simp\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs']\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shr_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shr\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n (value % Compiler.Constants.evmModulus) /\n 2 ^ (shift % Compiler.Constants.evmModulus)\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n (value % EvmYul.UInt256.size) / 2 ^ (shift % EvmYul.UInt256.size)\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs', Nat.shiftRight_eq_div_pow]\n change value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size) =\n value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size)\n rfl\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs']\n\nprivate theorem nat_land_0xFF (n : Nat) : Nat.land n 255 = n % 256 := by\n rw [show (255 : Nat) = 2 ^ 8 - 1 from by omega]\n exact Nat.and_two_pow_sub_one_eq_mod n 8\n\nset_option maxHeartbeats 16000000 in\nprivate theorem evalPureBuiltinViaEvmYulLean_byte_normalized (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n (if index % EvmYul.UInt256.size > 31 then some 0\n else some ((value % EvmYul.UInt256.size /\n 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) % 256)) := by\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.byteAt (EvmYul.UInt256.ofNat index) (EvmYul.UInt256.ofNat value))) = _\n by_cases hgt : index % EvmYul.UInt256.size > 31\n · have hgt' : EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256) := by\n show (31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val\n show (31 : Nat) < index % EvmYul.UInt256.size\n exact hgt\n simp [hgt, EvmYul.UInt256.byteAt, hgt', EvmYul.UInt256.toNat]\n · have hle' : ¬(EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256)) := by\n show ¬((31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val)\n show ¬((31 : Nat) < index % EvmYul.UInt256.size)\n exact hgt\n have hshift_small : (31 - index % EvmYul.UInt256.size) * 8 < EvmYul.UInt256.size := by\n unfold EvmYul.UInt256.size; omega\n have hguard : ¬ 256 ≤ (EvmYul.UInt256.ofNat\n ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)).val := by\n change ¬ 256 ≤ ((31 - index % EvmYul.UInt256.size) * 8) % EvmYul.UInt256.size\n rw [Nat.mod_eq_of_lt hshift_small]; omega\n unfold EvmYul.UInt256.byteAt\n rw [if_neg hle']\n show some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.land\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value)\n (EvmYul.UInt256.ofNat ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)))\n ⟨255⟩)) = _\n unfold EvmYul.UInt256.shiftRight\n rw [if_neg hguard]\n simp only [hgt, ite_false, EvmYul.UInt256.land, EvmYul.UInt256.toNat,\n EvmYul.UInt256.ofNat, Id.run, Fin.land, Fin.shiftRight, Fin.ofNat,\n Nat.shiftRight_eq_div_pow]\n rw [Nat.mod_eq_of_lt hshift_small]\n rw [show (255 : Nat) % EvmYul.UInt256.size = 255 from by unfold EvmYul.UInt256.size; omega]\n have hdiv_lt :\n value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8) <\n EvmYul.UInt256.size :=\n Nat.lt_of_le_of_lt (Nat.div_le_self _ _)\n (Nat.mod_lt value (by unfold EvmYul.UInt256.size; omega))\n rw [Nat.mod_eq_of_lt hdiv_lt]\n rw [nat_land_0xFF]\n have hmod256_lt_size :\n (value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) %\n 256 < EvmYul.UInt256.size :=\n Nat.lt_trans (Nat.mod_lt _ (by omega)) (by unfold EvmYul.UInt256.size; omega)\n rw [Nat.mod_eq_of_lt hmod256_lt_size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_byte_native (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n some (Verity.Core.Uint256.byte\n (Verity.Core.Uint256.ofNat (index % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n rw [evalPureBuiltinViaEvmYulLean_byte_normalized]\n have hindexMod :\n index % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n index % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n have hvalueMod :\n value % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n value % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n rw [uint256_size_eq_evmModulus]\n simp [Verity.Core.Uint256.byte, hindexMod, hvalueMod]\n by_cases hgt : 31 < index % Compiler.Constants.evmModulus\n · simp [hgt]\n · simp [hgt, Nat.shiftRight_eq_div_pow]\n rw [show (255 : Nat) = 2 ^ 8 - 1 by omega]\n rw [Nat.and_two_pow_sub_one_eq_mod]\n rw [show (2 ^ 8 : Nat) = 256 by norm_num]\n have hlt :\n (value % Compiler.Constants.evmModulus /\n 2 ^ ((31 - index % Compiler.Constants.evmModulus) * 8)) %\n 256 < Verity.Core.Uint256.modulus :=\n Nat.lt_trans (Nat.mod_lt _ (by decide : 0 < 256))\n (by norm_num [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS])\n rw [Nat.mod_eq_of_lt hlt]\n\nend Compiler.Proofs.YulGeneration.Backends\n"},"solution_diff":{"kind":"string","value":"@@ -104,6 +104,10 @@\n rw [← uint256_size_eq_evmModulus]\n rfl\n \n+private theorem toNat_fromBool (b : Bool) :\n+ EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\n+ cases b <;> rfl\n+\n private theorem uint256_lt_iff_nat_lt {a b : Nat}\n (ha : a < EvmYul.UInt256.size) (hb : b < EvmYul.UInt256.size) :\n ((⟨⟨a, ha⟩⟩ : EvmYul.UInt256) < ⟨⟨b, hb⟩⟩) ↔ (a < b) :=\n@@ -117,7 +121,18 @@\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n- ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := sorry\n+ ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n+ unfold EvmYul.UInt256.slt\n+ rw [toNat_fromBool]\n+ unfold EvmYul.UInt256.sltBool\n+ simp only [EvmYul.UInt256.toNat, ge_iff_le]\n+ have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n+ have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n+ simp only [uint256_lt_iff_nat_lt ha' hb']\n+ simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n+ Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n+ Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n+ split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n \n @[simp] theorem evalPureBuiltinViaEvmYulLean_slt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"slt\" [a, b] =\n@@ -170,7 +185,18 @@\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n- ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := sorry\n+ ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n+ unfold EvmYul.UInt256.sgt\n+ rw [toNat_fromBool]\n+ unfold EvmYul.UInt256.sgtBool\n+ simp only [EvmYul.UInt256.toNat, ge_iff_le]\n+ have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n+ have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n+ simp only [uint256_lt_iff_nat_lt hb' ha']\n+ simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n+ Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n+ Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n+ split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n \n @[simp] theorem evalPureBuiltinViaEvmYulLean_sgt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sgt\" [a, b] =\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21375,"cells":{"task_id":{"kind":"string","value":"ablate_72489ced2f65_1"},"challenge_id":{"kind":"string","value":"68b0dd09ec3a777a"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/YulGeneration/Backends/EvmYulLeanPureBuiltinLemmas.lean"},"theory":{"kind":"string","value":"EvmYulLeanPureBuiltinLemmas"},"variant":{"kind":"number","value":1,"string":"1"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":6,"string":"6"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"evalPureBuiltinViaEvmYulLean_or_native","depth":1,"n_commands":0,"n_lines":9,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.or) (n := 256)\n (word_lt_uint256_size a) (word_lt_uint256_size b)","n_chars":391,"n_subproofs":0,"n_tactics":9,"cyclomatic":1,"n_automation":0,"n_rewrites":4,"n_structural":1,"automation_only":false,"max_nesting":6},{"theorem_name":"evalPureBuiltinViaEvmYulLean_xor_native","depth":1,"n_commands":0,"n_lines":8,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rw [← uint256_size_eq_evmModulus]\n change some (((a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)) =\n some (a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size)\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)","n_chars":317,"n_subproofs":0,"n_tactics":8,"cyclomatic":1,"n_automation":0,"n_rewrites":4,"n_structural":1,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"theorem_name\": \"evalPureBuiltinViaEvmYulLean_or_native\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 9,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rw [← uint256_size_eq_evmModulus]\\n change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\\n EvmYul.UInt256.size)) =\\n some (Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\\n congr 1\\n rw [Nat.mod_eq_of_lt]\\n exact Nat.bitwise_lt_two_pow (f := Bool.or) (n := 256)\\n (word_lt_uint256_size a) (word_lt_uint256_size b)\",\n \"n_chars\": 391,\n \"n_subproofs\": 0,\n \"n_tactics\": 9,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 4,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n },\n {\n \"theorem_name\": \"evalPureBuiltinViaEvmYulLean_xor_native\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 8,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rw [← uint256_size_eq_evmModulus]\\n change some (((a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size) %\\n EvmYul.UInt256.size)) =\\n some (a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size)\\n congr 1\\n rw [Nat.mod_eq_of_lt]\\n exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)\",\n \"n_chars\": 317,\n \"n_subproofs\": 0,\n \"n_tactics\": 8,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 4,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"word_lt_uint256_size","text":"private theorem word_lt_uint256_size (x : Nat) :\n x % EvmYul.UInt256.size < 2 ^ 256 := by\n simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\n\n","fan_in":2,"n_lines":5,"n_chars":181,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":2,"n_rewrites":0,"n_structural":0,"automation_only":true,"max_nesting":2}],"string":"[\n {\n \"name\": \"word_lt_uint256_size\",\n \"text\": \"private theorem word_lt_uint256_size (x : Nat) :\\n x % EvmYul.UInt256.size < 2 ^ 256 := by\\n simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 5,\n \"n_chars\": 181,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": true,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"evalPureBuiltinViaEvmYulLean_or_native","fan_in":0,"n_deps_direct":2,"n_deps_transitive":2,"n_lines":13,"n_chars":600,"n_subproofs":0,"n_tactics":9,"cyclomatic":1,"n_automation":0,"n_rewrites":4,"n_structural":1,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"evalPureBuiltinViaEvmYulLean_or_native\",\n \"fan_in\": 0,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 2,\n \"n_lines\": 13,\n \"n_chars\": 600,\n \"n_subproofs\": 0,\n \"n_tactics\": 9,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 4,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas\nimport Mathlib.Data.Nat.Bitwise\nimport Verity.Core.Int256\nimport Verity.Core.Uint256\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nprivate theorem uint256_size_eq_evmModulus :\n EvmYul.UInt256.size = Compiler.Constants.evmModulus := by\n decide\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_add_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"add\" [a, b] =\n some ((a + b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a + Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a + b) % EvmYul.UInt256.size)\n simp [Fin.val_add, Nat.add_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sub_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sub\" [a, b] =\n some ((Compiler.Constants.evmModulus + (a % Compiler.Constants.evmModulus) -\n (b % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a - Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)\n have hsub :\n EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size =\n EvmYul.UInt256.size - b % EvmYul.UInt256.size + a % EvmYul.UInt256.size := by\n have hb : b % EvmYul.UInt256.size ≤ EvmYul.UInt256.size := by\n exact Nat.le_of_lt (Nat.mod_lt _ (by simp [EvmYul.UInt256.size]))\n omega\n simp [Fin.sub_def, Nat.add_mod, hsub]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mul_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mul\" [a, b] =\n some ((a * b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a * Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a * b) % EvmYul.UInt256.size)\n simp [Fin.mul_def, Nat.mul_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_div_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"div\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) / (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a / Fin.ofNat EvmYul.UInt256.size b).val) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) / (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0 <;> simp [hb]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mod\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) % (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) % (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0\n · have hb0val : ((EvmYul.UInt256.ofNat b).val).val = 0 := by\n change b % EvmYul.UInt256.size = 0\n exact hb\n have hb0 : (EvmYul.UInt256.ofNat b).val = 0 := Fin.ext hb0val\n simp [EvmYul.UInt256.mod, EvmYul.UInt256.toNat, hb, hb0]\n · have hb0 : ¬ (EvmYul.UInt256.ofNat b).val = 0 := by\n intro h\n exact hb (congrArg Fin.val h)\n rw [show EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b) =\n ⟨(EvmYul.UInt256.ofNat a).val % (EvmYul.UInt256.ofNat b).val⟩ by\n simp [EvmYul.UInt256.mod, hb0]]\n simp [hb, EvmYul.UInt256.toNat]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_eq_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"eq\" [a, b] =\n some (if a % Compiler.Constants.evmModulus = b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_iszero_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"iszero\" [a] =\n some (if a % Compiler.Constants.evmModulus = 0 then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_lt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"lt\" [a, b] =\n some (if a % Compiler.Constants.evmModulus < b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_gt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"gt\" [a, b] =\n some (if b % Compiler.Constants.evmModulus < a % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\nprivate theorem toNat_fromBool (b : Bool) :\n EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\n cases b <;> rfl\n\nprivate theorem uint256_lt_iff_nat_lt {a b : Nat}\n (ha : a < EvmYul.UInt256.size) (hb : b < EvmYul.UInt256.size) :\n ((⟨⟨a, ha⟩⟩ : EvmYul.UInt256) < ⟨⟨b, hb⟩⟩) ↔ (a < b) :=\n Iff.rfl\n\nprivate theorem slt_int256_eq_sltBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.slt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sltBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt ha' hb']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_slt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"slt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (slt_int256_eq_sltBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\nprivate theorem sgt_int256_eq_sgtBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.sgt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sgtBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt hb' ha']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sgt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sgt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (sgt_int256_eq_sgtBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sdiv_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sdiv\" [a, b] =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sdiv (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_div_toUint256_val_eq_uint256_sdiv\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_smod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"smod\" [a, b] =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.smod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_mod_toUint256_val_eq_uint256_smod\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sar_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"sar\" [shift, value] =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val := by\n have hs : shift % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt shift (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sar (EvmYul.UInt256.ofNat shift) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat shift =\n (⟨⟨shift % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hs⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_s :\n (shift % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n shift % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hs)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_s, hmod_v]\n exact (int256_sar_toUint256_val_eq_uint256_sar\n (shift % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hs hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_signextend_native (byteIdx value : Nat) :\n evalPureBuiltinViaEvmYulLean \"signextend\" [byteIdx, value] =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n have hb : byteIdx % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt byteIdx (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.signextend (EvmYul.UInt256.ofNat byteIdx) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val\n congr 1\n rw [show EvmYul.UInt256.ofNat byteIdx =\n (⟨⟨byteIdx % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_b :\n (byteIdx % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n byteIdx % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_b, hmod_v]\n exact (uint256_signextend_val_eq_uint256_signextend\n (byteIdx % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hb hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_and_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"and\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.and) (n := 256)\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt a (by decide : 0 < EvmYul.UInt256.size))\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt b (by decide : 0 < EvmYul.UInt256.size))\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_or_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"or\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := sorry\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_xor_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"xor\" [a, b] =\n some (Nat.xor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus)) := sorry\n\nprivate theorem xor_all_ones_uint256_word (a : Nat) :\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n calc\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n ((BitVec.ofNat 256 a) ^^^ BitVec.allOnes 256).toNat := by\n simp [BitVec.toNat_xor, EvmYul.UInt256.size]\n _ = (~~~(BitVec.ofNat 256 a)).toNat := by\n rw [BitVec.xor_allOnes]\n _ = EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n simp [BitVec.toNat_not, EvmYul.UInt256.size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_not_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (Nat.xor (a % Compiler.Constants.evmModulus)\n (Compiler.Constants.evmModulus - 1)) := by\n rw [← uint256_size_eq_evmModulus]\n change evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some ((a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1))\n have hsub : evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n change evalPureBuiltinViaEvmYulLean \"sub\" [EvmYul.UInt256.size - 1, a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size))\n rw [evalPureBuiltinViaEvmYulLean_sub_native]\n rw [← uint256_size_eq_evmModulus]\n have hs : 0 < EvmYul.UInt256.size := by simp [EvmYul.UInt256.size]\n have ha : a % EvmYul.UInt256.size < EvmYul.UInt256.size := Nat.mod_lt _ hs\n have hlt : EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) < EvmYul.UInt256.size := by\n omega\n have hmod :\n ((EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size -\n a % EvmYul.UInt256.size) % EvmYul.UInt256.size) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n have hsizeMinusOneMod :\n (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size = EvmYul.UInt256.size - 1 := by\n exact Nat.mod_eq_of_lt (by omega)\n rw [hsizeMinusOneMod]\n have harr :\n EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) - a % EvmYul.UInt256.size =\n EvmYul.UInt256.size +\n (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n omega\n rw [harr, Nat.add_mod_left, Nat.mod_eq_of_lt hlt]\n exact congrArg some hmod\n rw [hsub]\n simp [xor_all_ones_uint256_word]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shl_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shl\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n ((value % Compiler.Constants.evmModulus) *\n 2 ^ (shift % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftLeft (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n ((value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs', Nat.shiftLeft_eq]\n change (value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size) %\n EvmYul.UInt256.size =\n value * 2 ^ (shift % EvmYul.UInt256.size) % EvmYul.UInt256.size\n rw [Nat.mul_mod, Nat.mul_mod]\n simp\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs']\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shr_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shr\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n (value % Compiler.Constants.evmModulus) /\n 2 ^ (shift % Compiler.Constants.evmModulus)\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n (value % EvmYul.UInt256.size) / 2 ^ (shift % EvmYul.UInt256.size)\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs', Nat.shiftRight_eq_div_pow]\n change value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size) =\n value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size)\n rfl\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs']\n\nprivate theorem nat_land_0xFF (n : Nat) : Nat.land n 255 = n % 256 := by\n rw [show (255 : Nat) = 2 ^ 8 - 1 from by omega]\n exact Nat.and_two_pow_sub_one_eq_mod n 8\n\nset_option maxHeartbeats 16000000 in\nprivate theorem evalPureBuiltinViaEvmYulLean_byte_normalized (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n (if index % EvmYul.UInt256.size > 31 then some 0\n else some ((value % EvmYul.UInt256.size /\n 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) % 256)) := by\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.byteAt (EvmYul.UInt256.ofNat index) (EvmYul.UInt256.ofNat value))) = _\n by_cases hgt : index % EvmYul.UInt256.size > 31\n · have hgt' : EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256) := by\n show (31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val\n show (31 : Nat) < index % EvmYul.UInt256.size\n exact hgt\n simp [hgt, EvmYul.UInt256.byteAt, hgt', EvmYul.UInt256.toNat]\n · have hle' : ¬(EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256)) := by\n show ¬((31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val)\n show ¬((31 : Nat) < index % EvmYul.UInt256.size)\n exact hgt\n have hshift_small : (31 - index % EvmYul.UInt256.size) * 8 < EvmYul.UInt256.size := by\n unfold EvmYul.UInt256.size; omega\n have hguard : ¬ 256 ≤ (EvmYul.UInt256.ofNat\n ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)).val := by\n change ¬ 256 ≤ ((31 - index % EvmYul.UInt256.size) * 8) % EvmYul.UInt256.size\n rw [Nat.mod_eq_of_lt hshift_small]; omega\n unfold EvmYul.UInt256.byteAt\n rw [if_neg hle']\n show some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.land\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value)\n (EvmYul.UInt256.ofNat ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)))\n ⟨255⟩)) = _\n unfold EvmYul.UInt256.shiftRight\n rw [if_neg hguard]\n simp only [hgt, ite_false, EvmYul.UInt256.land, EvmYul.UInt256.toNat,\n EvmYul.UInt256.ofNat, Id.run, Fin.land, Fin.shiftRight, Fin.ofNat,\n Nat.shiftRight_eq_div_pow]\n rw [Nat.mod_eq_of_lt hshift_small]\n rw [show (255 : Nat) % EvmYul.UInt256.size = 255 from by unfold EvmYul.UInt256.size; omega]\n have hdiv_lt :\n value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8) <\n EvmYul.UInt256.size :=\n Nat.lt_of_le_of_lt (Nat.div_le_self _ _)\n (Nat.mod_lt value (by unfold EvmYul.UInt256.size; omega))\n rw [Nat.mod_eq_of_lt hdiv_lt]\n rw [nat_land_0xFF]\n have hmod256_lt_size :\n (value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) %\n 256 < EvmYul.UInt256.size :=\n Nat.lt_trans (Nat.mod_lt _ (by omega)) (by unfold EvmYul.UInt256.size; omega)\n rw [Nat.mod_eq_of_lt hmod256_lt_size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_byte_native (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n some (Verity.Core.Uint256.byte\n (Verity.Core.Uint256.ofNat (index % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n rw [evalPureBuiltinViaEvmYulLean_byte_normalized]\n have hindexMod :\n index % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n index % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n have hvalueMod :\n value % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n value % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n rw [uint256_size_eq_evmModulus]\n simp [Verity.Core.Uint256.byte, hindexMod, hvalueMod]\n by_cases hgt : 31 < index % Compiler.Constants.evmModulus\n · simp [hgt]\n · simp [hgt, Nat.shiftRight_eq_div_pow]\n rw [show (255 : Nat) = 2 ^ 8 - 1 by omega]\n rw [Nat.and_two_pow_sub_one_eq_mod]\n rw [show (2 ^ 8 : Nat) = 256 by norm_num]\n have hlt :\n (value % Compiler.Constants.evmModulus /\n 2 ^ ((31 - index % Compiler.Constants.evmModulus) * 8)) %\n 256 < Verity.Core.Uint256.modulus :=\n Nat.lt_trans (Nat.mod_lt _ (by decide : 0 < 256))\n (by norm_num [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS])\n rw [Nat.mod_eq_of_lt hlt]\n\nend Compiler.Proofs.YulGeneration.Backends\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas\nimport Mathlib.Data.Nat.Bitwise\nimport Verity.Core.Int256\nimport Verity.Core.Uint256\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nprivate theorem uint256_size_eq_evmModulus :\n EvmYul.UInt256.size = Compiler.Constants.evmModulus := by\n decide\n\nprivate theorem word_lt_uint256_size (x : Nat) :\n x % EvmYul.UInt256.size < 2 ^ 256 := by\n simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_add_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"add\" [a, b] =\n some ((a + b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a + Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a + b) % EvmYul.UInt256.size)\n simp [Fin.val_add, Nat.add_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sub_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sub\" [a, b] =\n some ((Compiler.Constants.evmModulus + (a % Compiler.Constants.evmModulus) -\n (b % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a - Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)\n have hsub :\n EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size =\n EvmYul.UInt256.size - b % EvmYul.UInt256.size + a % EvmYul.UInt256.size := by\n have hb : b % EvmYul.UInt256.size ≤ EvmYul.UInt256.size := by\n exact Nat.le_of_lt (Nat.mod_lt _ (by simp [EvmYul.UInt256.size]))\n omega\n simp [Fin.sub_def, Nat.add_mod, hsub]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mul_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mul\" [a, b] =\n some ((a * b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a * Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a * b) % EvmYul.UInt256.size)\n simp [Fin.mul_def, Nat.mul_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_div_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"div\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) / (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a / Fin.ofNat EvmYul.UInt256.size b).val) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) / (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0 <;> simp [hb]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mod\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) % (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) % (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0\n · have hb0val : ((EvmYul.UInt256.ofNat b).val).val = 0 := by\n change b % EvmYul.UInt256.size = 0\n exact hb\n have hb0 : (EvmYul.UInt256.ofNat b).val = 0 := Fin.ext hb0val\n simp [EvmYul.UInt256.mod, EvmYul.UInt256.toNat, hb, hb0]\n · have hb0 : ¬ (EvmYul.UInt256.ofNat b).val = 0 := by\n intro h\n exact hb (congrArg Fin.val h)\n rw [show EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b) =\n ⟨(EvmYul.UInt256.ofNat a).val % (EvmYul.UInt256.ofNat b).val⟩ by\n simp [EvmYul.UInt256.mod, hb0]]\n simp [hb, EvmYul.UInt256.toNat]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_eq_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"eq\" [a, b] =\n some (if a % Compiler.Constants.evmModulus = b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_iszero_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"iszero\" [a] =\n some (if a % Compiler.Constants.evmModulus = 0 then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_lt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"lt\" [a, b] =\n some (if a % Compiler.Constants.evmModulus < b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_gt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"gt\" [a, b] =\n some (if b % Compiler.Constants.evmModulus < a % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\nprivate theorem toNat_fromBool (b : Bool) :\n EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\n cases b <;> rfl\n\nprivate theorem uint256_lt_iff_nat_lt {a b : Nat}\n (ha : a < EvmYul.UInt256.size) (hb : b < EvmYul.UInt256.size) :\n ((⟨⟨a, ha⟩⟩ : EvmYul.UInt256) < ⟨⟨b, hb⟩⟩) ↔ (a < b) :=\n Iff.rfl\n\nprivate theorem slt_int256_eq_sltBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.slt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sltBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt ha' hb']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_slt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"slt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (slt_int256_eq_sltBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\nprivate theorem sgt_int256_eq_sgtBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.sgt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sgtBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt hb' ha']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sgt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sgt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (sgt_int256_eq_sgtBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sdiv_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sdiv\" [a, b] =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sdiv (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_div_toUint256_val_eq_uint256_sdiv\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_smod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"smod\" [a, b] =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.smod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_mod_toUint256_val_eq_uint256_smod\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sar_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"sar\" [shift, value] =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val := by\n have hs : shift % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt shift (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sar (EvmYul.UInt256.ofNat shift) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat shift =\n (⟨⟨shift % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hs⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_s :\n (shift % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n shift % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hs)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_s, hmod_v]\n exact (int256_sar_toUint256_val_eq_uint256_sar\n (shift % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hs hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_signextend_native (byteIdx value : Nat) :\n evalPureBuiltinViaEvmYulLean \"signextend\" [byteIdx, value] =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n have hb : byteIdx % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt byteIdx (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.signextend (EvmYul.UInt256.ofNat byteIdx) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val\n congr 1\n rw [show EvmYul.UInt256.ofNat byteIdx =\n (⟨⟨byteIdx % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_b :\n (byteIdx % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n byteIdx % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_b, hmod_v]\n exact (uint256_signextend_val_eq_uint256_signextend\n (byteIdx % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hb hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_and_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"and\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.and) (n := 256)\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt a (by decide : 0 < EvmYul.UInt256.size))\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt b (by decide : 0 < EvmYul.UInt256.size))\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_or_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"or\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.or) (n := 256)\n (word_lt_uint256_size a) (word_lt_uint256_size b)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_xor_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"xor\" [a, b] =\n some (Nat.xor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)) =\n some (a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size)\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)\n\nprivate theorem xor_all_ones_uint256_word (a : Nat) :\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n calc\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n ((BitVec.ofNat 256 a) ^^^ BitVec.allOnes 256).toNat := by\n simp [BitVec.toNat_xor, EvmYul.UInt256.size]\n _ = (~~~(BitVec.ofNat 256 a)).toNat := by\n rw [BitVec.xor_allOnes]\n _ = EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n simp [BitVec.toNat_not, EvmYul.UInt256.size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_not_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (Nat.xor (a % Compiler.Constants.evmModulus)\n (Compiler.Constants.evmModulus - 1)) := by\n rw [← uint256_size_eq_evmModulus]\n change evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some ((a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1))\n have hsub : evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n change evalPureBuiltinViaEvmYulLean \"sub\" [EvmYul.UInt256.size - 1, a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size))\n rw [evalPureBuiltinViaEvmYulLean_sub_native]\n rw [← uint256_size_eq_evmModulus]\n have hs : 0 < EvmYul.UInt256.size := by simp [EvmYul.UInt256.size]\n have ha : a % EvmYul.UInt256.size < EvmYul.UInt256.size := Nat.mod_lt _ hs\n have hlt : EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) < EvmYul.UInt256.size := by\n omega\n have hmod :\n ((EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size -\n a % EvmYul.UInt256.size) % EvmYul.UInt256.size) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n have hsizeMinusOneMod :\n (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size = EvmYul.UInt256.size - 1 := by\n exact Nat.mod_eq_of_lt (by omega)\n rw [hsizeMinusOneMod]\n have harr :\n EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) - a % EvmYul.UInt256.size =\n EvmYul.UInt256.size +\n (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n omega\n rw [harr, Nat.add_mod_left, Nat.mod_eq_of_lt hlt]\n exact congrArg some hmod\n rw [hsub]\n simp [xor_all_ones_uint256_word]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shl_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shl\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n ((value % Compiler.Constants.evmModulus) *\n 2 ^ (shift % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftLeft (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n ((value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs', Nat.shiftLeft_eq]\n change (value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size) %\n EvmYul.UInt256.size =\n value * 2 ^ (shift % EvmYul.UInt256.size) % EvmYul.UInt256.size\n rw [Nat.mul_mod, Nat.mul_mod]\n simp\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs']\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shr_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shr\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n (value % Compiler.Constants.evmModulus) /\n 2 ^ (shift % Compiler.Constants.evmModulus)\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n (value % EvmYul.UInt256.size) / 2 ^ (shift % EvmYul.UInt256.size)\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs', Nat.shiftRight_eq_div_pow]\n change value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size) =\n value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size)\n rfl\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs']\n\nprivate theorem nat_land_0xFF (n : Nat) : Nat.land n 255 = n % 256 := by\n rw [show (255 : Nat) = 2 ^ 8 - 1 from by omega]\n exact Nat.and_two_pow_sub_one_eq_mod n 8\n\nset_option maxHeartbeats 16000000 in\nprivate theorem evalPureBuiltinViaEvmYulLean_byte_normalized (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n (if index % EvmYul.UInt256.size > 31 then some 0\n else some ((value % EvmYul.UInt256.size /\n 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) % 256)) := by\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.byteAt (EvmYul.UInt256.ofNat index) (EvmYul.UInt256.ofNat value))) = _\n by_cases hgt : index % EvmYul.UInt256.size > 31\n · have hgt' : EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256) := by\n show (31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val\n show (31 : Nat) < index % EvmYul.UInt256.size\n exact hgt\n simp [hgt, EvmYul.UInt256.byteAt, hgt', EvmYul.UInt256.toNat]\n · have hle' : ¬(EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256)) := by\n show ¬((31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val)\n show ¬((31 : Nat) < index % EvmYul.UInt256.size)\n exact hgt\n have hshift_small : (31 - index % EvmYul.UInt256.size) * 8 < EvmYul.UInt256.size := by\n unfold EvmYul.UInt256.size; omega\n have hguard : ¬ 256 ≤ (EvmYul.UInt256.ofNat\n ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)).val := by\n change ¬ 256 ≤ ((31 - index % EvmYul.UInt256.size) * 8) % EvmYul.UInt256.size\n rw [Nat.mod_eq_of_lt hshift_small]; omega\n unfold EvmYul.UInt256.byteAt\n rw [if_neg hle']\n show some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.land\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value)\n (EvmYul.UInt256.ofNat ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)))\n ⟨255⟩)) = _\n unfold EvmYul.UInt256.shiftRight\n rw [if_neg hguard]\n simp only [hgt, ite_false, EvmYul.UInt256.land, EvmYul.UInt256.toNat,\n EvmYul.UInt256.ofNat, Id.run, Fin.land, Fin.shiftRight, Fin.ofNat,\n Nat.shiftRight_eq_div_pow]\n rw [Nat.mod_eq_of_lt hshift_small]\n rw [show (255 : Nat) % EvmYul.UInt256.size = 255 from by unfold EvmYul.UInt256.size; omega]\n have hdiv_lt :\n value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8) <\n EvmYul.UInt256.size :=\n Nat.lt_of_le_of_lt (Nat.div_le_self _ _)\n (Nat.mod_lt value (by unfold EvmYul.UInt256.size; omega))\n rw [Nat.mod_eq_of_lt hdiv_lt]\n rw [nat_land_0xFF]\n have hmod256_lt_size :\n (value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) %\n 256 < EvmYul.UInt256.size :=\n Nat.lt_trans (Nat.mod_lt _ (by omega)) (by unfold EvmYul.UInt256.size; omega)\n rw [Nat.mod_eq_of_lt hmod256_lt_size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_byte_native (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n some (Verity.Core.Uint256.byte\n (Verity.Core.Uint256.ofNat (index % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n rw [evalPureBuiltinViaEvmYulLean_byte_normalized]\n have hindexMod :\n index % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n index % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n have hvalueMod :\n value % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n value % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n rw [uint256_size_eq_evmModulus]\n simp [Verity.Core.Uint256.byte, hindexMod, hvalueMod]\n by_cases hgt : 31 < index % Compiler.Constants.evmModulus\n · simp [hgt]\n · simp [hgt, Nat.shiftRight_eq_div_pow]\n rw [show (255 : Nat) = 2 ^ 8 - 1 by omega]\n rw [Nat.and_two_pow_sub_one_eq_mod]\n rw [show (2 ^ 8 : Nat) = 256 by norm_num]\n have hlt :\n (value % Compiler.Constants.evmModulus /\n 2 ^ ((31 - index % Compiler.Constants.evmModulus) * 8)) %\n 256 < Verity.Core.Uint256.modulus :=\n Nat.lt_trans (Nat.mod_lt _ (by decide : 0 < 256))\n (by norm_num [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS])\n rw [Nat.mod_eq_of_lt hlt]\n\nend Compiler.Proofs.YulGeneration.Backends\n"},"solution_diff":{"kind":"string","value":"@@ -10,6 +10,10 @@\n EvmYul.UInt256.size = Compiler.Constants.evmModulus := by\n decide\n \n+private theorem word_lt_uint256_size (x : Nat) :\n+ x % EvmYul.UInt256.size < 2 ^ 256 := by\n+ simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\n+\n @[simp] theorem evalPureBuiltinViaEvmYulLean_add_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"add\" [a, b] =\n some ((a + b) % Compiler.Constants.evmModulus) := by\n@@ -404,11 +408,26 @@\n \n @[simp] theorem evalPureBuiltinViaEvmYulLean_or_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"or\" [a, b] =\n- some ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := sorry\n+ some ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n+ rw [← uint256_size_eq_evmModulus]\n+ change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n+ EvmYul.UInt256.size)) =\n+ some (Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n+ congr 1\n+ rw [Nat.mod_eq_of_lt]\n+ exact Nat.bitwise_lt_two_pow (f := Bool.or) (n := 256)\n+ (word_lt_uint256_size a) (word_lt_uint256_size b)\n \n @[simp] theorem evalPureBuiltinViaEvmYulLean_xor_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"xor\" [a, b] =\n- some (Nat.xor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus)) := sorry\n+ some (Nat.xor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus)) := by\n+ rw [← uint256_size_eq_evmModulus]\n+ change some (((a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size) %\n+ EvmYul.UInt256.size)) =\n+ some (a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size)\n+ congr 1\n+ rw [Nat.mod_eq_of_lt]\n+ exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)\n \n private theorem xor_all_ones_uint256_word (a : Nat) :\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21376,"cells":{"task_id":{"kind":"string","value":"ablate_72489ced2f65_2"},"challenge_id":{"kind":"string","value":"519da257b383f582"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/YulGeneration/Backends/EvmYulLeanPureBuiltinLemmas.lean"},"theory":{"kind":"string","value":"EvmYulLeanPureBuiltinLemmas"},"variant":{"kind":"number","value":2,"string":"2"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":6,"string":"6"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"evalPureBuiltinViaEvmYulLean_not_native","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n rw [← uint256_size_eq_evmModulus]\n change evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some ((a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1))\n have hsub : evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n change evalPureBuiltinViaEvmYulLean \"sub\" [EvmYul.UInt256.size - 1, a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size))\n rw [evalPureBuiltinViaEvmYulLean_sub_native]\n rw [← uint256_size_eq_evmModulus]\n have hs : 0 < EvmYul.UInt256.size := by simp [EvmYul.UInt256.size]\n have ha : a % EvmYul.UInt256.size < EvmYul.UInt256.size := Nat.mod_lt _ hs\n have hlt : EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) < EvmYul.UInt256.size := by\n omega\n have hmod :\n ((EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size -\n a % EvmYul.UInt256.size) % EvmYul.UInt256.size) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n have hsizeMinusOneMod :\n (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size = EvmYul.UInt256.size - 1 := by\n exact Nat.mod_eq_of_lt (by omega)\n rw [hsizeMinusOneMod]\n have harr :\n EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) - a % EvmYul.UInt256.size =\n EvmYul.UInt256.size +\n (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n omega\n rw [harr, Nat.add_mod_left, Nat.mod_eq_of_lt hlt]\n exact congrArg some hmod\n rw [hsub]\n simp [xor_all_ones_uint256_word]","n_chars":1548,"n_subproofs":7,"n_tactics":31,"cyclomatic":1,"n_automation":5,"n_rewrites":8,"n_structural":2,"automation_only":false,"max_nesting":14}],"string":"[\n {\n \"theorem_name\": \"evalPureBuiltinViaEvmYulLean_not_native\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n rw [← uint256_size_eq_evmModulus]\\n change evalPureBuiltinViaEvmYulLean \\\"not\\\" [a] =\\n some ((a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1))\\n have hsub : evalPureBuiltinViaEvmYulLean \\\"not\\\" [a] =\\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\\n change evalPureBuiltinViaEvmYulLean \\\"sub\\\" [EvmYul.UInt256.size - 1, a] =\\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size))\\n rw [evalPureBuiltinViaEvmYulLean_sub_native]\\n rw [← uint256_size_eq_evmModulus]\\n have hs : 0 < EvmYul.UInt256.size := by simp [EvmYul.UInt256.size]\\n have ha : a % EvmYul.UInt256.size < EvmYul.UInt256.size := Nat.mod_lt _ hs\\n have hlt : EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) < EvmYul.UInt256.size := by\\n omega\\n have hmod :\\n ((EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size -\\n a % EvmYul.UInt256.size) % EvmYul.UInt256.size) =\\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\\n have hsizeMinusOneMod :\\n (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size = EvmYul.UInt256.size - 1 := by\\n exact Nat.mod_eq_of_lt (by omega)\\n rw [hsizeMinusOneMod]\\n have harr :\\n EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) - a % EvmYul.UInt256.size =\\n EvmYul.UInt256.size +\\n (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\\n omega\\n rw [harr, Nat.add_mod_left, Nat.mod_eq_of_lt hlt]\\n exact congrArg some hmod\\n rw [hsub]\\n simp [xor_all_ones_uint256_word]\",\n \"n_chars\": 1548,\n \"n_subproofs\": 7,\n \"n_tactics\": 31,\n \"cyclomatic\": 1,\n \"n_automation\": 5,\n \"n_rewrites\": 8,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 14\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"xor_all_ones_uint256_word","text":"private theorem xor_all_ones_uint256_word (a : Nat) :\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n calc\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n ((BitVec.ofNat 256 a) ^^^ BitVec.allOnes 256).toNat := by\n simp [BitVec.toNat_xor, EvmYul.UInt256.size]\n _ = (~~~(BitVec.ofNat 256 a)).toNat := by\n rw [BitVec.xor_allOnes]\n _ = EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n simp [BitVec.toNat_not, EvmYul.UInt256.size]\n\n","fan_in":1,"n_lines":13,"n_chars":560,"n_subproofs":0,"n_tactics":9,"cyclomatic":1,"n_automation":2,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"xor_all_ones_uint256_word\",\n \"text\": \"private theorem xor_all_ones_uint256_word (a : Nat) :\\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\\n calc\\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\\n ((BitVec.ofNat 256 a) ^^^ BitVec.allOnes 256).toNat := by\\n simp [BitVec.toNat_xor, EvmYul.UInt256.size]\\n _ = (~~~(BitVec.ofNat 256 a)).toNat := by\\n rw [BitVec.xor_allOnes]\\n _ = EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\\n simp [BitVec.toNat_not, EvmYul.UInt256.size]\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 13,\n \"n_chars\": 560,\n \"n_subproofs\": 0,\n \"n_tactics\": 9,\n \"cyclomatic\": 1,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"evalPureBuiltinViaEvmYulLean_not_native","fan_in":0,"n_deps_direct":3,"n_deps_transitive":3,"n_lines":36,"n_chars":1766,"n_subproofs":7,"n_tactics":31,"cyclomatic":1,"n_automation":5,"n_rewrites":8,"n_structural":2,"automation_only":false,"max_nesting":14}],"string":"[\n {\n \"name\": \"evalPureBuiltinViaEvmYulLean_not_native\",\n \"fan_in\": 0,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 3,\n \"n_lines\": 36,\n \"n_chars\": 1766,\n \"n_subproofs\": 7,\n \"n_tactics\": 31,\n \"cyclomatic\": 1,\n \"n_automation\": 5,\n \"n_rewrites\": 8,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 14\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas\nimport Mathlib.Data.Nat.Bitwise\nimport Verity.Core.Int256\nimport Verity.Core.Uint256\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nprivate theorem uint256_size_eq_evmModulus :\n EvmYul.UInt256.size = Compiler.Constants.evmModulus := by\n decide\n\nprivate theorem word_lt_uint256_size (x : Nat) :\n x % EvmYul.UInt256.size < 2 ^ 256 := by\n simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_add_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"add\" [a, b] =\n some ((a + b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a + Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a + b) % EvmYul.UInt256.size)\n simp [Fin.val_add, Nat.add_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sub_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sub\" [a, b] =\n some ((Compiler.Constants.evmModulus + (a % Compiler.Constants.evmModulus) -\n (b % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a - Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)\n have hsub :\n EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size =\n EvmYul.UInt256.size - b % EvmYul.UInt256.size + a % EvmYul.UInt256.size := by\n have hb : b % EvmYul.UInt256.size ≤ EvmYul.UInt256.size := by\n exact Nat.le_of_lt (Nat.mod_lt _ (by simp [EvmYul.UInt256.size]))\n omega\n simp [Fin.sub_def, Nat.add_mod, hsub]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mul_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mul\" [a, b] =\n some ((a * b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a * Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a * b) % EvmYul.UInt256.size)\n simp [Fin.mul_def, Nat.mul_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_div_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"div\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) / (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a / Fin.ofNat EvmYul.UInt256.size b).val) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) / (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0 <;> simp [hb]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mod\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) % (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) % (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0\n · have hb0val : ((EvmYul.UInt256.ofNat b).val).val = 0 := by\n change b % EvmYul.UInt256.size = 0\n exact hb\n have hb0 : (EvmYul.UInt256.ofNat b).val = 0 := Fin.ext hb0val\n simp [EvmYul.UInt256.mod, EvmYul.UInt256.toNat, hb, hb0]\n · have hb0 : ¬ (EvmYul.UInt256.ofNat b).val = 0 := by\n intro h\n exact hb (congrArg Fin.val h)\n rw [show EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b) =\n ⟨(EvmYul.UInt256.ofNat a).val % (EvmYul.UInt256.ofNat b).val⟩ by\n simp [EvmYul.UInt256.mod, hb0]]\n simp [hb, EvmYul.UInt256.toNat]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_eq_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"eq\" [a, b] =\n some (if a % Compiler.Constants.evmModulus = b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_iszero_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"iszero\" [a] =\n some (if a % Compiler.Constants.evmModulus = 0 then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_lt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"lt\" [a, b] =\n some (if a % Compiler.Constants.evmModulus < b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_gt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"gt\" [a, b] =\n some (if b % Compiler.Constants.evmModulus < a % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\nprivate theorem toNat_fromBool (b : Bool) :\n EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\n cases b <;> rfl\n\nprivate theorem uint256_lt_iff_nat_lt {a b : Nat}\n (ha : a < EvmYul.UInt256.size) (hb : b < EvmYul.UInt256.size) :\n ((⟨⟨a, ha⟩⟩ : EvmYul.UInt256) < ⟨⟨b, hb⟩⟩) ↔ (a < b) :=\n Iff.rfl\n\nprivate theorem slt_int256_eq_sltBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.slt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sltBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt ha' hb']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_slt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"slt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (slt_int256_eq_sltBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\nprivate theorem sgt_int256_eq_sgtBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.sgt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sgtBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt hb' ha']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sgt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sgt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (sgt_int256_eq_sgtBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sdiv_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sdiv\" [a, b] =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sdiv (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_div_toUint256_val_eq_uint256_sdiv\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_smod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"smod\" [a, b] =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.smod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_mod_toUint256_val_eq_uint256_smod\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sar_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"sar\" [shift, value] =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val := by\n have hs : shift % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt shift (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sar (EvmYul.UInt256.ofNat shift) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat shift =\n (⟨⟨shift % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hs⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_s :\n (shift % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n shift % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hs)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_s, hmod_v]\n exact (int256_sar_toUint256_val_eq_uint256_sar\n (shift % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hs hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_signextend_native (byteIdx value : Nat) :\n evalPureBuiltinViaEvmYulLean \"signextend\" [byteIdx, value] =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n have hb : byteIdx % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt byteIdx (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.signextend (EvmYul.UInt256.ofNat byteIdx) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val\n congr 1\n rw [show EvmYul.UInt256.ofNat byteIdx =\n (⟨⟨byteIdx % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_b :\n (byteIdx % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n byteIdx % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_b, hmod_v]\n exact (uint256_signextend_val_eq_uint256_signextend\n (byteIdx % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hb hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_and_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"and\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.and) (n := 256)\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt a (by decide : 0 < EvmYul.UInt256.size))\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt b (by decide : 0 < EvmYul.UInt256.size))\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_or_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"or\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.or) (n := 256)\n (word_lt_uint256_size a) (word_lt_uint256_size b)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_xor_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"xor\" [a, b] =\n some (Nat.xor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)) =\n some (a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size)\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_not_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (Nat.xor (a % Compiler.Constants.evmModulus)\n (Compiler.Constants.evmModulus - 1)) := sorry\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shl_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shl\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n ((value % Compiler.Constants.evmModulus) *\n 2 ^ (shift % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftLeft (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n ((value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs', Nat.shiftLeft_eq]\n change (value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size) %\n EvmYul.UInt256.size =\n value * 2 ^ (shift % EvmYul.UInt256.size) % EvmYul.UInt256.size\n rw [Nat.mul_mod, Nat.mul_mod]\n simp\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs']\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shr_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shr\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n (value % Compiler.Constants.evmModulus) /\n 2 ^ (shift % Compiler.Constants.evmModulus)\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n (value % EvmYul.UInt256.size) / 2 ^ (shift % EvmYul.UInt256.size)\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs', Nat.shiftRight_eq_div_pow]\n change value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size) =\n value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size)\n rfl\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs']\n\nprivate theorem nat_land_0xFF (n : Nat) : Nat.land n 255 = n % 256 := by\n rw [show (255 : Nat) = 2 ^ 8 - 1 from by omega]\n exact Nat.and_two_pow_sub_one_eq_mod n 8\n\nset_option maxHeartbeats 16000000 in\nprivate theorem evalPureBuiltinViaEvmYulLean_byte_normalized (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n (if index % EvmYul.UInt256.size > 31 then some 0\n else some ((value % EvmYul.UInt256.size /\n 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) % 256)) := by\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.byteAt (EvmYul.UInt256.ofNat index) (EvmYul.UInt256.ofNat value))) = _\n by_cases hgt : index % EvmYul.UInt256.size > 31\n · have hgt' : EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256) := by\n show (31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val\n show (31 : Nat) < index % EvmYul.UInt256.size\n exact hgt\n simp [hgt, EvmYul.UInt256.byteAt, hgt', EvmYul.UInt256.toNat]\n · have hle' : ¬(EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256)) := by\n show ¬((31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val)\n show ¬((31 : Nat) < index % EvmYul.UInt256.size)\n exact hgt\n have hshift_small : (31 - index % EvmYul.UInt256.size) * 8 < EvmYul.UInt256.size := by\n unfold EvmYul.UInt256.size; omega\n have hguard : ¬ 256 ≤ (EvmYul.UInt256.ofNat\n ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)).val := by\n change ¬ 256 ≤ ((31 - index % EvmYul.UInt256.size) * 8) % EvmYul.UInt256.size\n rw [Nat.mod_eq_of_lt hshift_small]; omega\n unfold EvmYul.UInt256.byteAt\n rw [if_neg hle']\n show some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.land\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value)\n (EvmYul.UInt256.ofNat ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)))\n ⟨255⟩)) = _\n unfold EvmYul.UInt256.shiftRight\n rw [if_neg hguard]\n simp only [hgt, ite_false, EvmYul.UInt256.land, EvmYul.UInt256.toNat,\n EvmYul.UInt256.ofNat, Id.run, Fin.land, Fin.shiftRight, Fin.ofNat,\n Nat.shiftRight_eq_div_pow]\n rw [Nat.mod_eq_of_lt hshift_small]\n rw [show (255 : Nat) % EvmYul.UInt256.size = 255 from by unfold EvmYul.UInt256.size; omega]\n have hdiv_lt :\n value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8) <\n EvmYul.UInt256.size :=\n Nat.lt_of_le_of_lt (Nat.div_le_self _ _)\n (Nat.mod_lt value (by unfold EvmYul.UInt256.size; omega))\n rw [Nat.mod_eq_of_lt hdiv_lt]\n rw [nat_land_0xFF]\n have hmod256_lt_size :\n (value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) %\n 256 < EvmYul.UInt256.size :=\n Nat.lt_trans (Nat.mod_lt _ (by omega)) (by unfold EvmYul.UInt256.size; omega)\n rw [Nat.mod_eq_of_lt hmod256_lt_size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_byte_native (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n some (Verity.Core.Uint256.byte\n (Verity.Core.Uint256.ofNat (index % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n rw [evalPureBuiltinViaEvmYulLean_byte_normalized]\n have hindexMod :\n index % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n index % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n have hvalueMod :\n value % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n value % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n rw [uint256_size_eq_evmModulus]\n simp [Verity.Core.Uint256.byte, hindexMod, hvalueMod]\n by_cases hgt : 31 < index % Compiler.Constants.evmModulus\n · simp [hgt]\n · simp [hgt, Nat.shiftRight_eq_div_pow]\n rw [show (255 : Nat) = 2 ^ 8 - 1 by omega]\n rw [Nat.and_two_pow_sub_one_eq_mod]\n rw [show (2 ^ 8 : Nat) = 256 by norm_num]\n have hlt :\n (value % Compiler.Constants.evmModulus /\n 2 ^ ((31 - index % Compiler.Constants.evmModulus) * 8)) %\n 256 < Verity.Core.Uint256.modulus :=\n Nat.lt_trans (Nat.mod_lt _ (by decide : 0 < 256))\n (by norm_num [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS])\n rw [Nat.mod_eq_of_lt hlt]\n\nend Compiler.Proofs.YulGeneration.Backends\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas\nimport Mathlib.Data.Nat.Bitwise\nimport Verity.Core.Int256\nimport Verity.Core.Uint256\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nprivate theorem uint256_size_eq_evmModulus :\n EvmYul.UInt256.size = Compiler.Constants.evmModulus := by\n decide\n\nprivate theorem word_lt_uint256_size (x : Nat) :\n x % EvmYul.UInt256.size < 2 ^ 256 := by\n simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_add_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"add\" [a, b] =\n some ((a + b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a + Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a + b) % EvmYul.UInt256.size)\n simp [Fin.val_add, Nat.add_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sub_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sub\" [a, b] =\n some ((Compiler.Constants.evmModulus + (a % Compiler.Constants.evmModulus) -\n (b % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a - Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)\n have hsub :\n EvmYul.UInt256.size + a % EvmYul.UInt256.size - b % EvmYul.UInt256.size =\n EvmYul.UInt256.size - b % EvmYul.UInt256.size + a % EvmYul.UInt256.size := by\n have hb : b % EvmYul.UInt256.size ≤ EvmYul.UInt256.size := by\n exact Nat.le_of_lt (Nat.mod_lt _ (by simp [EvmYul.UInt256.size]))\n omega\n simp [Fin.sub_def, Nat.add_mod, hsub]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mul_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mul\" [a, b] =\n some ((a * b) % Compiler.Constants.evmModulus) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a * Fin.ofNat EvmYul.UInt256.size b).val) =\n some ((a * b) % EvmYul.UInt256.size)\n simp [Fin.mul_def, Nat.mul_mod]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_div_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"div\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) / (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some ((Fin.ofNat EvmYul.UInt256.size a / Fin.ofNat EvmYul.UInt256.size b).val) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) / (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0 <;> simp [hb]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_mod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"mod\" [a, b] =\n some (if b % Compiler.Constants.evmModulus = 0 then 0 else\n (a % Compiler.Constants.evmModulus) % (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if b % EvmYul.UInt256.size = 0 then 0 else\n (a % EvmYul.UInt256.size) % (b % EvmYul.UInt256.size))\n by_cases hb : b % EvmYul.UInt256.size = 0\n · have hb0val : ((EvmYul.UInt256.ofNat b).val).val = 0 := by\n change b % EvmYul.UInt256.size = 0\n exact hb\n have hb0 : (EvmYul.UInt256.ofNat b).val = 0 := Fin.ext hb0val\n simp [EvmYul.UInt256.mod, EvmYul.UInt256.toNat, hb, hb0]\n · have hb0 : ¬ (EvmYul.UInt256.ofNat b).val = 0 := by\n intro h\n exact hb (congrArg Fin.val h)\n rw [show EvmYul.UInt256.mod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b) =\n ⟨(EvmYul.UInt256.ofNat a).val % (EvmYul.UInt256.ofNat b).val⟩ by\n simp [EvmYul.UInt256.mod, hb0]]\n simp [hb, EvmYul.UInt256.toNat]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_eq_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"eq\" [a, b] =\n some (if a % Compiler.Constants.evmModulus = b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_iszero_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"iszero\" [a] =\n some (if a % Compiler.Constants.evmModulus = 0 then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_lt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"lt\" [a, b] =\n some (if a % Compiler.Constants.evmModulus < b % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_gt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"gt\" [a, b] =\n some (if b % Compiler.Constants.evmModulus < a % Compiler.Constants.evmModulus then 1 else 0) := by\n rw [← uint256_size_eq_evmModulus]\n rfl\n\nprivate theorem toNat_fromBool (b : Bool) :\n EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\n cases b <;> rfl\n\nprivate theorem uint256_lt_iff_nat_lt {a b : Nat}\n (ha : a < EvmYul.UInt256.size) (hb : b < EvmYul.UInt256.size) :\n ((⟨⟨a, ha⟩⟩ : EvmYul.UInt256) < ⟨⟨b, hb⟩⟩) ↔ (a < b) :=\n Iff.rfl\n\nprivate theorem slt_int256_eq_sltBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.slt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sltBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt ha' hb']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_slt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"slt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.slt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (slt_int256_eq_sltBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\nprivate theorem sgt_int256_eq_sgtBool (a b : Nat)\n (ha : a < Compiler.Constants.evmModulus)\n (hb : b < Compiler.Constants.evmModulus) :\n (if Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨b, hb⟩) <\n Verity.Core.Int256.toInt (Verity.Core.Int256.ofUint256 ⟨a, ha⟩)\n then (1 : Nat) else 0) =\n (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt ⟨⟨a, by simpa [uint256_size_eq_evmModulus] using ha⟩⟩\n ⟨⟨b, by simpa [uint256_size_eq_evmModulus] using hb⟩⟩)) := by\n unfold EvmYul.UInt256.sgt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sgtBool\n simp only [EvmYul.UInt256.toNat, ge_iff_le]\n have ha' : a < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using ha\n have hb' : b < EvmYul.UInt256.size := by simpa [uint256_size_eq_evmModulus] using hb\n simp only [uint256_lt_iff_nat_lt hb' ha']\n simp only [Verity.Core.Int256.toInt, Verity.Core.Int256.ofUint256,\n Verity.Core.Int256.signBit, Verity.Core.Int256.modulus,\n Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS]\n split_ifs <;> simp_all [Compiler.Constants.evmModulus, EvmYul.UInt256.size] <;> omega\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sgt_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sgt\" [a, b] =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0) := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sgt (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (if Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus))) <\n Verity.Core.Int256.toInt\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n then 1 else 0)\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (sgt_int256_eq_sgtBool\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sdiv_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"sdiv\" [a, b] =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sdiv (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.div\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_div_toUint256_val_eq_uint256_sdiv\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_smod_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"smod\" [a, b] =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val := by\n have ha : a % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt a (by unfold Compiler.Constants.evmModulus; omega)\n have hb : b % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt b (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.smod (EvmYul.UInt256.ofNat a) (EvmYul.UInt256.ofNat b))) =\n some (Verity.Core.Int256.mod\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (a % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (b % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat a =\n (⟨⟨a % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using ha⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat b =\n (⟨⟨b % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_a :\n (a % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n a % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using ha)\n have hmod_b :\n (b % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n b % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_a, hmod_b]\n exact (int256_mod_toUint256_val_eq_uint256_smod\n (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus) ha hb).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_sar_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"sar\" [shift, value] =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val := by\n have hs : shift % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt shift (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.sar (EvmYul.UInt256.ofNat shift) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Int256.sar\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (shift % Compiler.Constants.evmModulus)))\n (Verity.Core.Int256.ofUint256\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus)))).toUint256.val\n congr 1\n rw [show EvmYul.UInt256.ofNat shift =\n (⟨⟨shift % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hs⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_s :\n (shift % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n shift % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hs)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_s, hmod_v]\n exact (int256_sar_toUint256_val_eq_uint256_sar\n (shift % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hs hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_signextend_native (byteIdx value : Nat) :\n evalPureBuiltinViaEvmYulLean \"signextend\" [byteIdx, value] =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n have hb : byteIdx % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt byteIdx (by unfold Compiler.Constants.evmModulus; omega)\n have hv : value % Compiler.Constants.evmModulus < Compiler.Constants.evmModulus :=\n Nat.mod_lt value (by unfold Compiler.Constants.evmModulus; omega)\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.signextend (EvmYul.UInt256.ofNat byteIdx) (EvmYul.UInt256.ofNat value))) =\n some (Verity.Core.Uint256.signextend\n (Verity.Core.Uint256.ofNat (byteIdx % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val\n congr 1\n rw [show EvmYul.UInt256.ofNat byteIdx =\n (⟨⟨byteIdx % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hb⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n rw [show EvmYul.UInt256.ofNat value =\n (⟨⟨value % Compiler.Constants.evmModulus, by\n simpa [uint256_size_eq_evmModulus] using hv⟩⟩ : EvmYul.UInt256) by\n simp only [EvmYul.UInt256.ofNat, Id.run]; congr 1]\n have hmod_b :\n (byteIdx % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n byteIdx % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hb)\n have hmod_v :\n (value % Compiler.Constants.evmModulus) % Verity.Core.UINT256_MODULUS =\n value % Compiler.Constants.evmModulus := by\n exact Nat.mod_eq_of_lt (by simpa [Compiler.Constants.evmModulus, Verity.Core.UINT256_MODULUS] using hv)\n simp only [Verity.Core.Uint256.ofNat, Verity.Core.Uint256.modulus, hmod_b, hmod_v]\n exact (uint256_signextend_val_eq_uint256_signextend\n (byteIdx % Compiler.Constants.evmModulus) (value % Compiler.Constants.evmModulus) hb hv).symm\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_and_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"and\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) &&& (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.and (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.and) (n := 256)\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt a (by decide : 0 < EvmYul.UInt256.size))\n (by simpa [EvmYul.UInt256.size] using Nat.mod_lt b (by decide : 0 < EvmYul.UInt256.size))\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_or_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"or\" [a, b] =\n some ((a % Compiler.Constants.evmModulus) ||| (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size)) =\n some (Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b % EvmYul.UInt256.size))\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.bitwise_lt_two_pow (f := Bool.or) (n := 256)\n (word_lt_uint256_size a) (word_lt_uint256_size b)\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_xor_native (a b : Nat) :\n evalPureBuiltinViaEvmYulLean \"xor\" [a, b] =\n some (Nat.xor (a % Compiler.Constants.evmModulus) (b % Compiler.Constants.evmModulus)) := by\n rw [← uint256_size_eq_evmModulus]\n change some (((a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size) %\n EvmYul.UInt256.size)) =\n some (a % EvmYul.UInt256.size ^^^ b % EvmYul.UInt256.size)\n congr 1\n rw [Nat.mod_eq_of_lt]\n exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)\n\nprivate theorem xor_all_ones_uint256_word (a : Nat) :\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n calc\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n ((BitVec.ofNat 256 a) ^^^ BitVec.allOnes 256).toNat := by\n simp [BitVec.toNat_xor, EvmYul.UInt256.size]\n _ = (~~~(BitVec.ofNat 256 a)).toNat := by\n rw [BitVec.xor_allOnes]\n _ = EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n simp [BitVec.toNat_not, EvmYul.UInt256.size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_not_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (Nat.xor (a % Compiler.Constants.evmModulus)\n (Compiler.Constants.evmModulus - 1)) := by\n rw [← uint256_size_eq_evmModulus]\n change evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some ((a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1))\n have hsub : evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n change evalPureBuiltinViaEvmYulLean \"sub\" [EvmYul.UInt256.size - 1, a] =\n some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size))\n rw [evalPureBuiltinViaEvmYulLean_sub_native]\n rw [← uint256_size_eq_evmModulus]\n have hs : 0 < EvmYul.UInt256.size := by simp [EvmYul.UInt256.size]\n have ha : a % EvmYul.UInt256.size < EvmYul.UInt256.size := Nat.mod_lt _ hs\n have hlt : EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) < EvmYul.UInt256.size := by\n omega\n have hmod :\n ((EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size -\n a % EvmYul.UInt256.size) % EvmYul.UInt256.size) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n have hsizeMinusOneMod :\n (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size = EvmYul.UInt256.size - 1 := by\n exact Nat.mod_eq_of_lt (by omega)\n rw [hsizeMinusOneMod]\n have harr :\n EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) - a % EvmYul.UInt256.size =\n EvmYul.UInt256.size +\n (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n omega\n rw [harr, Nat.add_mod_left, Nat.mod_eq_of_lt hlt]\n exact congrArg some hmod\n rw [hsub]\n simp [xor_all_ones_uint256_word]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shl_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shl\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n ((value % Compiler.Constants.evmModulus) *\n 2 ^ (shift % Compiler.Constants.evmModulus)) % Compiler.Constants.evmModulus\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftLeft (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n ((value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size)) %\n EvmYul.UInt256.size\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs', Nat.shiftLeft_eq]\n change (value % EvmYul.UInt256.size) * 2 ^ (shift % EvmYul.UInt256.size) %\n EvmYul.UInt256.size =\n value * 2 ^ (shift % EvmYul.UInt256.size) % EvmYul.UInt256.size\n rw [Nat.mul_mod, Nat.mul_mod]\n simp\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftLeft, EvmYul.UInt256.toNat, hs']\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_shr_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shr\" [shift, value] =\n some (if shift % Compiler.Constants.evmModulus < 256 then\n (value % Compiler.Constants.evmModulus) /\n 2 ^ (shift % Compiler.Constants.evmModulus)\n else\n 0) := by\n rw [← uint256_size_eq_evmModulus]\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value) (EvmYul.UInt256.ofNat shift))) =\n some (if shift % EvmYul.UInt256.size < 256 then\n (value % EvmYul.UInt256.size) / 2 ^ (shift % EvmYul.UInt256.size)\n else\n 0)\n by_cases hs : shift % EvmYul.UInt256.size < 256\n · have hs' : ¬ 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change ¬ 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_le_of_lt hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs', Nat.shiftRight_eq_div_pow]\n change value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size) =\n value % EvmYul.UInt256.size / 2 ^ (shift % EvmYul.UInt256.size)\n rfl\n · have hs' : 256 ≤ (EvmYul.UInt256.ofNat shift).val := by\n change 256 ≤ shift % EvmYul.UInt256.size\n exact Nat.not_lt.mp hs\n simp [hs, EvmYul.UInt256.shiftRight, EvmYul.UInt256.toNat, hs']\n\nprivate theorem nat_land_0xFF (n : Nat) : Nat.land n 255 = n % 256 := by\n rw [show (255 : Nat) = 2 ^ 8 - 1 from by omega]\n exact Nat.and_two_pow_sub_one_eq_mod n 8\n\nset_option maxHeartbeats 16000000 in\nprivate theorem evalPureBuiltinViaEvmYulLean_byte_normalized (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n (if index % EvmYul.UInt256.size > 31 then some 0\n else some ((value % EvmYul.UInt256.size /\n 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) % 256)) := by\n change some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.byteAt (EvmYul.UInt256.ofNat index) (EvmYul.UInt256.ofNat value))) = _\n by_cases hgt : index % EvmYul.UInt256.size > 31\n · have hgt' : EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256) := by\n show (31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val\n show (31 : Nat) < index % EvmYul.UInt256.size\n exact hgt\n simp [hgt, EvmYul.UInt256.byteAt, hgt', EvmYul.UInt256.toNat]\n · have hle' : ¬(EvmYul.UInt256.ofNat index > (⟨31⟩ : EvmYul.UInt256)) := by\n show ¬((31 : Fin EvmYul.UInt256.size) < (EvmYul.UInt256.ofNat index).val)\n show ¬((31 : Nat) < index % EvmYul.UInt256.size)\n exact hgt\n have hshift_small : (31 - index % EvmYul.UInt256.size) * 8 < EvmYul.UInt256.size := by\n unfold EvmYul.UInt256.size; omega\n have hguard : ¬ 256 ≤ (EvmYul.UInt256.ofNat\n ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)).val := by\n change ¬ 256 ≤ ((31 - index % EvmYul.UInt256.size) * 8) % EvmYul.UInt256.size\n rw [Nat.mod_eq_of_lt hshift_small]; omega\n unfold EvmYul.UInt256.byteAt\n rw [if_neg hle']\n show some (EvmYul.UInt256.toNat\n (EvmYul.UInt256.land\n (EvmYul.UInt256.shiftRight (EvmYul.UInt256.ofNat value)\n (EvmYul.UInt256.ofNat ((31 - (EvmYul.UInt256.ofNat index).toNat) * 8)))\n ⟨255⟩)) = _\n unfold EvmYul.UInt256.shiftRight\n rw [if_neg hguard]\n simp only [hgt, ite_false, EvmYul.UInt256.land, EvmYul.UInt256.toNat,\n EvmYul.UInt256.ofNat, Id.run, Fin.land, Fin.shiftRight, Fin.ofNat,\n Nat.shiftRight_eq_div_pow]\n rw [Nat.mod_eq_of_lt hshift_small]\n rw [show (255 : Nat) % EvmYul.UInt256.size = 255 from by unfold EvmYul.UInt256.size; omega]\n have hdiv_lt :\n value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8) <\n EvmYul.UInt256.size :=\n Nat.lt_of_le_of_lt (Nat.div_le_self _ _)\n (Nat.mod_lt value (by unfold EvmYul.UInt256.size; omega))\n rw [Nat.mod_eq_of_lt hdiv_lt]\n rw [nat_land_0xFF]\n have hmod256_lt_size :\n (value % EvmYul.UInt256.size / 2 ^ ((31 - index % EvmYul.UInt256.size) * 8)) %\n 256 < EvmYul.UInt256.size :=\n Nat.lt_trans (Nat.mod_lt _ (by omega)) (by unfold EvmYul.UInt256.size; omega)\n rw [Nat.mod_eq_of_lt hmod256_lt_size]\n\n@[simp] theorem evalPureBuiltinViaEvmYulLean_byte_native (index value : Nat) :\n evalPureBuiltinViaEvmYulLean \"byte\" [index, value] =\n some (Verity.Core.Uint256.byte\n (Verity.Core.Uint256.ofNat (index % Compiler.Constants.evmModulus))\n (Verity.Core.Uint256.ofNat (value % Compiler.Constants.evmModulus))).val := by\n rw [evalPureBuiltinViaEvmYulLean_byte_normalized]\n have hindexMod :\n index % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n index % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n have hvalueMod :\n value % Compiler.Constants.evmModulus % Verity.Core.Uint256.modulus =\n value % Compiler.Constants.evmModulus := by\n simp [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS, Compiler.Constants.evmModulus]\n rw [uint256_size_eq_evmModulus]\n simp [Verity.Core.Uint256.byte, hindexMod, hvalueMod]\n by_cases hgt : 31 < index % Compiler.Constants.evmModulus\n · simp [hgt]\n · simp [hgt, Nat.shiftRight_eq_div_pow]\n rw [show (255 : Nat) = 2 ^ 8 - 1 by omega]\n rw [Nat.and_two_pow_sub_one_eq_mod]\n rw [show (2 ^ 8 : Nat) = 256 by norm_num]\n have hlt :\n (value % Compiler.Constants.evmModulus /\n 2 ^ ((31 - index % Compiler.Constants.evmModulus) * 8)) %\n 256 < Verity.Core.Uint256.modulus :=\n Nat.lt_trans (Nat.mod_lt _ (by decide : 0 < 256))\n (by norm_num [Verity.Core.Uint256.modulus, Verity.Core.UINT256_MODULUS])\n rw [Nat.mod_eq_of_lt hlt]\n\nend Compiler.Proofs.YulGeneration.Backends\n"},"solution_diff":{"kind":"string","value":"@@ -429,10 +429,52 @@\n rw [Nat.mod_eq_of_lt]\n exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)\n \n+private theorem xor_all_ones_uint256_word (a : Nat) :\n+ (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n+ EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n+ calc\n+ (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n+ ((BitVec.ofNat 256 a) ^^^ BitVec.allOnes 256).toNat := by\n+ simp [BitVec.toNat_xor, EvmYul.UInt256.size]\n+ _ = (~~~(BitVec.ofNat 256 a)).toNat := by\n+ rw [BitVec.xor_allOnes]\n+ _ = EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n+ simp [BitVec.toNat_not, EvmYul.UInt256.size]\n+\n @[simp] theorem evalPureBuiltinViaEvmYulLean_not_native (a : Nat) :\n evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (Nat.xor (a % Compiler.Constants.evmModulus)\n- (Compiler.Constants.evmModulus - 1)) := sorry\n+ (Compiler.Constants.evmModulus - 1)) := by\n+ rw [← uint256_size_eq_evmModulus]\n+ change evalPureBuiltinViaEvmYulLean \"not\" [a] =\n+ some ((a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1))\n+ have hsub : evalPureBuiltinViaEvmYulLean \"not\" [a] =\n+ some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n+ change evalPureBuiltinViaEvmYulLean \"sub\" [EvmYul.UInt256.size - 1, a] =\n+ some (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size))\n+ rw [evalPureBuiltinViaEvmYulLean_sub_native]\n+ rw [← uint256_size_eq_evmModulus]\n+ have hs : 0 < EvmYul.UInt256.size := by simp [EvmYul.UInt256.size]\n+ have ha : a % EvmYul.UInt256.size < EvmYul.UInt256.size := Nat.mod_lt _ hs\n+ have hlt : EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) < EvmYul.UInt256.size := by\n+ omega\n+ have hmod :\n+ ((EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size -\n+ a % EvmYul.UInt256.size) % EvmYul.UInt256.size) =\n+ EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n+ have hsizeMinusOneMod :\n+ (EvmYul.UInt256.size - 1) % EvmYul.UInt256.size = EvmYul.UInt256.size - 1 := by\n+ exact Nat.mod_eq_of_lt (by omega)\n+ rw [hsizeMinusOneMod]\n+ have harr :\n+ EvmYul.UInt256.size + (EvmYul.UInt256.size - 1) - a % EvmYul.UInt256.size =\n+ EvmYul.UInt256.size +\n+ (EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size)) := by\n+ omega\n+ rw [harr, Nat.add_mod_left, Nat.mod_eq_of_lt hlt]\n+ exact congrArg some hmod\n+ rw [hsub]\n+ simp [xor_all_ones_uint256_word]\n \n @[simp] theorem evalPureBuiltinViaEvmYulLean_shl_native (shift value : Nat) :\n evalPureBuiltinViaEvmYulLean \"shl\" [shift, value] =\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21377,"cells":{"task_id":{"kind":"string","value":"ablate_5f3c738a4fec_0"},"challenge_id":{"kind":"string","value":"471501b8c4ba359e"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/CEISafety.lean"},"theory":{"kind":"string","value":"CEISafety"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":1,"string":"1"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"ceiProofBackedExecution_checked_empty_body","depth":1,"n_commands":0,"n_lines":5,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n by\n refine ceiProofBackedExecution_of_checker rfl ?_ rfl rfl rfl\n change stmtListCEIViolation [] false = none\n simp [stmtListCEIViolation]","n_chars":150,"n_subproofs":0,"n_tactics":4,"cyclomatic":1,"n_automation":5,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"ceiProofBackedExecution_checked_empty_body\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 5,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n by\\n refine ceiProofBackedExecution_of_checker rfl ?_ rfl rfl rfl\\n change stmtListCEIViolation [] false = none\\n simp [stmtListCEIViolation]\",\n \"n_chars\": 150,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 5,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"ceiProofBackedExecution_of_checker","text":"/-- Bridge the concrete facts emitted by the macro/checker into the public CEI\nexecution theorem. Escape hatches are hypotheses rather than hidden premises. -/\ntheorem ceiProofBackedExecution_of_checker\n {fn : FunctionSpec}\n (hAnnotated : fn.ceiSafe = true)\n (hChecked : stmtListCEIViolation fn.body false = none)\n (hAllow : fn.allowPostInteractionWrites = false)\n (hLock : fn.nonReentrantLock = none)\n (hLocal : fn.localObligations = []) :\n CEIProofBackedExecution fn :=\n { annotated := hAnnotated\n executionSafe := hChecked\n trustExitsClosed :=\n { noPostInteractionWriteOptOut := hAllow\n noNonReentrantRuntimeGuard := hLock\n noLocalUnsafeObligations := hLocal } }\n\n","fan_in":1,"n_lines":18,"n_chars":714,"n_subproofs":0,"n_tactics":6,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"ceiProofBackedExecution_of_checker\",\n \"text\": \"/-- Bridge the concrete facts emitted by the macro/checker into the public CEI\\nexecution theorem. Escape hatches are hypotheses rather than hidden premises. -/\\ntheorem ceiProofBackedExecution_of_checker\\n {fn : FunctionSpec}\\n (hAnnotated : fn.ceiSafe = true)\\n (hChecked : stmtListCEIViolation fn.body false = none)\\n (hAllow : fn.allowPostInteractionWrites = false)\\n (hLock : fn.nonReentrantLock = none)\\n (hLocal : fn.localObligations = []) :\\n CEIProofBackedExecution fn :=\\n { annotated := hAnnotated\\n executionSafe := hChecked\\n trustExitsClosed :=\\n { noPostInteractionWriteOptOut := hAllow\\n noNonReentrantRuntimeGuard := hLock\\n noLocalUnsafeObligations := hLocal } }\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 18,\n \"n_chars\": 714,\n \"n_subproofs\": 0,\n \"n_tactics\": 6,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"ceiProofBackedExecution_checked_empty_body","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":16,"n_chars":548,"n_subproofs":0,"n_tactics":4,"cyclomatic":1,"n_automation":5,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"ceiProofBackedExecution_checked_empty_body\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 16,\n \"n_chars\": 548,\n \"n_subproofs\": 0,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 5,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.CompilationModel.Validation\n\n/-!\nProof-layer CEI safety surface.\n\n`stmtListCEIViolation` is the compiler checker used before code generation.\nThis module gives that checker a public proof-facing meaning: a function has\nproof-backed CEI execution safety exactly when the checker accepts its body and\nthe recognized trust exits are absent at the function boundary.\n\nScope: this certifies *single-function* Checks-Effects-Interactions ordering\nonly. It is **not** a cross-function reentrancy defense — a CEI-clean function\ncan still hand control to a callee that re-enters a sibling entrypoint while\nstate is mid-update (the Midnight `take`/`liquidate` class). Cross-function\nreentrancy is owned by the separate fail-closed gate\n`Compiler.CompilationModel.validateReentrancyDisposition`, whose sound\naccept-set is `nonreentrant(<lock>)` or `reentrancy_trusted` — explicitly *not*\n`cei_safe`/`allow_post_interaction_writes`.\n-/\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler.CompilationModel\n\n/-- Execution-level CEI claim for a function body: along the source statement\norder recognized by the compiler, no persistent state write is reachable after\nan external interaction barrier. -/\ndef CEIExecutionSafe (fn : FunctionSpec) : Prop :=\n stmtListCEIViolation fn.body false = none\n\n/-- Explicit CEI trust-exit obligations. A proof-backed `cei_safe` function must\nnot rely on the untyped post-interaction-write opt-out, the generated\n`nonreentrant` runtime guard, or local unsafe/refinement obligations. -/\nstructure CEITrustExitsClosed (fn : FunctionSpec) : Prop where\n noPostInteractionWriteOptOut : fn.allowPostInteractionWrites = false\n noNonReentrantRuntimeGuard : fn.nonReentrantLock = none\n noLocalUnsafeObligations : fn.localObligations = []\n\n/-- The public proof-backed `cei_safe` contract: the annotation is present, the\ncompiler CEI checker accepted the body, and all trust exits are closed. -/\nstructure CEIProofBackedExecution (fn : FunctionSpec) : Prop where\n annotated : fn.ceiSafe = true\n executionSafe : CEIExecutionSafe fn\n trustExitsClosed : CEITrustExitsClosed fn\n\n/-- Smoke theorem for the public bridge: an explicit `cei_safe` function whose\nbody is accepted by the CEI checker discharges the execution theorem without\nany escape hatch premise. -/\ntheorem ceiProofBackedExecution_checked_empty_body :\n CEIProofBackedExecution\n { name := \"checkedEmptyBody\"\n params := []\n returnType := none\n body := []\n ceiSafe := true } := sorry\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.CompilationModel.Validation\n\n/-!\nProof-layer CEI safety surface.\n\n`stmtListCEIViolation` is the compiler checker used before code generation.\nThis module gives that checker a public proof-facing meaning: a function has\nproof-backed CEI execution safety exactly when the checker accepts its body and\nthe recognized trust exits are absent at the function boundary.\n\nScope: this certifies *single-function* Checks-Effects-Interactions ordering\nonly. It is **not** a cross-function reentrancy defense — a CEI-clean function\ncan still hand control to a callee that re-enters a sibling entrypoint while\nstate is mid-update (the Midnight `take`/`liquidate` class). Cross-function\nreentrancy is owned by the separate fail-closed gate\n`Compiler.CompilationModel.validateReentrancyDisposition`, whose sound\naccept-set is `nonreentrant(<lock>)` or `reentrancy_trusted` — explicitly *not*\n`cei_safe`/`allow_post_interaction_writes`.\n-/\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler.CompilationModel\n\n/-- Execution-level CEI claim for a function body: along the source statement\norder recognized by the compiler, no persistent state write is reachable after\nan external interaction barrier. -/\ndef CEIExecutionSafe (fn : FunctionSpec) : Prop :=\n stmtListCEIViolation fn.body false = none\n\n/-- Explicit CEI trust-exit obligations. A proof-backed `cei_safe` function must\nnot rely on the untyped post-interaction-write opt-out, the generated\n`nonreentrant` runtime guard, or local unsafe/refinement obligations. -/\nstructure CEITrustExitsClosed (fn : FunctionSpec) : Prop where\n noPostInteractionWriteOptOut : fn.allowPostInteractionWrites = false\n noNonReentrantRuntimeGuard : fn.nonReentrantLock = none\n noLocalUnsafeObligations : fn.localObligations = []\n\n/-- The public proof-backed `cei_safe` contract: the annotation is present, the\ncompiler CEI checker accepted the body, and all trust exits are closed. -/\nstructure CEIProofBackedExecution (fn : FunctionSpec) : Prop where\n annotated : fn.ceiSafe = true\n executionSafe : CEIExecutionSafe fn\n trustExitsClosed : CEITrustExitsClosed fn\n\n/-- Bridge the concrete facts emitted by the macro/checker into the public CEI\nexecution theorem. Escape hatches are hypotheses rather than hidden premises. -/\ntheorem ceiProofBackedExecution_of_checker\n {fn : FunctionSpec}\n (hAnnotated : fn.ceiSafe = true)\n (hChecked : stmtListCEIViolation fn.body false = none)\n (hAllow : fn.allowPostInteractionWrites = false)\n (hLock : fn.nonReentrantLock = none)\n (hLocal : fn.localObligations = []) :\n CEIProofBackedExecution fn :=\n { annotated := hAnnotated\n executionSafe := hChecked\n trustExitsClosed :=\n { noPostInteractionWriteOptOut := hAllow\n noNonReentrantRuntimeGuard := hLock\n noLocalUnsafeObligations := hLocal } }\n\n/-- Smoke theorem for the public bridge: an explicit `cei_safe` function whose\nbody is accepted by the CEI checker discharges the execution theorem without\nany escape hatch premise. -/\ntheorem ceiProofBackedExecution_checked_empty_body :\n CEIProofBackedExecution\n { name := \"checkedEmptyBody\"\n params := []\n returnType := none\n body := []\n ceiSafe := true } :=\n by\n refine ceiProofBackedExecution_of_checker rfl ?_ rfl rfl rfl\n change stmtListCEIViolation [] false = none\n simp [stmtListCEIViolation]\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -43,6 +43,23 @@\n executionSafe : CEIExecutionSafe fn\n trustExitsClosed : CEITrustExitsClosed fn\n \n+/-- Bridge the concrete facts emitted by the macro/checker into the public CEI\n+execution theorem. Escape hatches are hypotheses rather than hidden premises. -/\n+theorem ceiProofBackedExecution_of_checker\n+ {fn : FunctionSpec}\n+ (hAnnotated : fn.ceiSafe = true)\n+ (hChecked : stmtListCEIViolation fn.body false = none)\n+ (hAllow : fn.allowPostInteractionWrites = false)\n+ (hLock : fn.nonReentrantLock = none)\n+ (hLocal : fn.localObligations = []) :\n+ CEIProofBackedExecution fn :=\n+ { annotated := hAnnotated\n+ executionSafe := hChecked\n+ trustExitsClosed :=\n+ { noPostInteractionWriteOptOut := hAllow\n+ noNonReentrantRuntimeGuard := hLock\n+ noLocalUnsafeObligations := hLocal } }\n+\n /-- Smoke theorem for the public bridge: an explicit `cei_safe` function whose\n body is accepted by the CEI checker discharges the execution theorem without\n any escape hatch premise. -/\n@@ -52,7 +69,11 @@\n params := []\n returnType := none\n body := []\n- ceiSafe := true } := sorry\n+ ceiSafe := true } :=\n+ by\n+ refine ceiProofBackedExecution_of_checker rfl ?_ rfl rfl rfl\n+ change stmtListCEIViolation [] false = none\n+ simp [stmtListCEIViolation]\n \n end Compiler.Proofs.IRGeneration\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21378,"cells":{"task_id":{"kind":"string","value":"ablate_81701029c1fb_0"},"challenge_id":{"kind":"string","value":"c06abb9f27def0da"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean"},"theory":{"kind":"string","value":"Safe"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":6,"string":"6"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"bridgedSafeStmts_assignKeccak_of_exprCompileCore","depth":1,"n_commands":0,"n_lines":7,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n BridgedSafeStmts.storage (by\n intro stmt hMem\n simp only [List.mem_singleton] at hMem\n subst stmt\n exact BridgedSourceStorageStmt.pureBinding\n (bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore hOffset hSize))","n_chars":240,"n_subproofs":0,"n_tactics":6,"cyclomatic":1,"n_automation":1,"n_rewrites":1,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"theorem_name\": \"bridgedSafeStmts_assignKeccak_of_exprCompileCore\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 7,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n BridgedSafeStmts.storage (by\\n intro stmt hMem\\n simp only [List.mem_singleton] at hMem\\n subst stmt\\n exact BridgedSourceStorageStmt.pureBinding\\n (bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore hOffset hSize))\",\n \"n_chars\": 240,\n \"n_subproofs\": 0,\n \"n_tactics\": 6,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 1,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore","text":"/-- An assignment whose RHS is syntactic `keccak256(offset, size)` is a native\n pure-binding source statement when the offset and size arguments are\n compile-core expressions. -/\ntheorem bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.assignVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.assignVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\n","fan_in":1,"n_lines":15,"n_chars":705,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore\",\n \"text\": \"/-- An assignment whose RHS is syntactic `keccak256(offset, size)` is a native\\n pure-binding source statement when the offset and size arguments are\\n compile-core expressions. -/\\ntheorem bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore\\n {name : String} {offset size : Expr}\\n (hOffset :\\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\\n (hSize :\\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\\n BridgedSourcePureBindingStmt\\n (.assignVar name (.keccak256 offset size)) :=\\n BridgedSourcePureBindingStmt.assignVar name (.keccak256 offset size)\\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 15,\n \"n_chars\": 705,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"bridgedSafeStmts_assignKeccak_of_exprCompileCore","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":20,"n_chars":930,"n_subproofs":0,"n_tactics":6,"cyclomatic":1,"n_automation":1,"n_rewrites":1,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"bridgedSafeStmts_assignKeccak_of_exprCompileCore\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 20,\n \"n_chars\": 930,\n \"n_subproofs\": 0,\n \"n_tactics\": 6,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 1,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\n/-- Singleton native safe-body package for `name := keccak256(offset,size)`\n with compile-core offset and size arguments. -/\ntheorem bridgedSafeStmts_assignKeccak_of_exprCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {internalRetNames : List String}\n {isInternal : Bool} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n [Stmt.assignVar name (.keccak256 offset size)] := sorry\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\n/-- An assignment whose RHS is syntactic `keccak256(offset, size)` is a native\n pure-binding source statement when the offset and size arguments are\n compile-core expressions. -/\ntheorem bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.assignVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.assignVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\n/-- Singleton native safe-body package for `name := keccak256(offset,size)`\n with compile-core offset and size arguments. -/\ntheorem bridgedSafeStmts_assignKeccak_of_exprCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {internalRetNames : List String}\n {isInternal : Bool} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n [Stmt.assignVar name (.keccak256 offset size)] :=\n BridgedSafeStmts.storage (by\n intro stmt hMem\n simp only [List.mem_singleton] at hMem\n subst stmt\n exact BridgedSourceStorageStmt.pureBinding\n (bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore hOffset hSize))\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\n"},"solution_diff":{"kind":"string","value":"@@ -172,6 +172,20 @@\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n \n+/-- An assignment whose RHS is syntactic `keccak256(offset, size)` is a native\n+ pure-binding source statement when the offset and size arguments are\n+ compile-core expressions. -/\n+theorem bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore\n+ {name : String} {offset size : Expr}\n+ (hOffset :\n+ _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n+ (hSize :\n+ _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n+ BridgedSourcePureBindingStmt\n+ (.assignVar name (.keccak256 offset size)) :=\n+ BridgedSourcePureBindingStmt.assignVar name (.keccak256 offset size)\n+ (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n+\n /-- Singleton native safe-body package for `name := keccak256(offset,size)`\n with compile-core offset and size arguments. -/\n theorem bridgedSafeStmts_assignKeccak_of_exprCompileCore\n@@ -183,7 +197,13 @@\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n- [Stmt.assignVar name (.keccak256 offset size)] := sorry\n+ [Stmt.assignVar name (.keccak256 offset size)] :=\n+ BridgedSafeStmts.storage (by\n+ intro stmt hMem\n+ simp only [List.mem_singleton] at hMem\n+ subst stmt\n+ exact BridgedSourceStorageStmt.pureBinding\n+ (bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore hOffset hSize))\n \n private def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21379,"cells":{"task_id":{"kind":"string","value":"ablate_81701029c1fb_1"},"challenge_id":{"kind":"string","value":"7e86793a38eea6c2"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean"},"theory":{"kind":"string","value":"Safe"},"variant":{"kind":"number","value":1,"string":"1"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":6,"string":"6"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore","depth":1,"n_commands":0,"n_lines":24,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction hTerminal with\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope hRest =>\n exact .cons (bridgedExternalRawLogReturn hValue)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | stop hRest =>\n exact .cons bridgedExternalRawLogStop\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\n exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)","n_chars":1164,"n_subproofs":0,"n_tactics":24,"cyclomatic":2,"n_automation":0,"n_rewrites":0,"n_structural":9,"automation_only":false,"max_nesting":10},{"theorem_name":"bridgedSafeStmts_externalCompileCore","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n BridgedSafeStmts.externalRecursiveRawLog\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hCore)","n_chars":134,"n_subproofs":0,"n_tactics":3,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"theorem_name\": \"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 24,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction hTerminal with\\n | letVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\\n | assignVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\\n | require_ hCond _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogRequire hCond) ih\\n | return_ hValue _hScope hRest =>\\n exact .cons (bridgedExternalRawLogReturn hValue)\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\\n | stop hRest =>\\n exact .cons bridgedExternalRawLogStop\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\\n | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\\n exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\",\n \"n_chars\": 1164,\n \"n_subproofs\": 0,\n \"n_tactics\": 24,\n \"cyclomatic\": 2,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 9,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"bridgedSafeStmts_externalCompileCore\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n BridgedSafeStmts.externalRecursiveRawLog\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hCore)\",\n \"n_chars\": 134,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore","text":"/-- Source compile-core statement lists are covered by the recursive external\n raw-log fragment: pure bindings route through the storage/body base\n predicate, requires and terminators are direct body cases, and direct\n memory/transient writes route through the memory-write extension. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hCore with\n | nil =>\n exact .nil\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogReturn hValue) ih\n | stop _hRest ih =>\n exact .cons bridgedExternalRawLogStop ih\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n\n","fan_in":2,"n_lines":31,"n_chars":1499,"n_subproofs":0,"n_tactics":18,"cyclomatic":2,"n_automation":0,"n_rewrites":0,"n_structural":9,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\",\n \"text\": \"/-- Source compile-core statement lists are covered by the recursive external\\n raw-log fragment: pure bindings route through the storage/body base\\n predicate, requires and terminators are direct body cases, and direct\\n memory/transient writes route through the memory-write extension. -/\\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n {fields : List Field} {errors : List ErrorDef}\\n {dynamicSource : DynamicDataSource} {scope : List String}\\n {stmts : List Stmt}\\n (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\\n scope stmts) :\\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\\n dynamicSource stmts := by\\n induction hCore with\\n | nil =>\\n exact .nil\\n | letVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\\n | assignVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\\n | require_ hCond _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogRequire hCond) ih\\n | return_ hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogReturn hValue) ih\\n | stop _hRest ih =>\\n exact .cons bridgedExternalRawLogStop ih\\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 31,\n \"n_chars\": 1499,\n \"n_subproofs\": 0,\n \"n_tactics\": 18,\n \"cyclomatic\": 2,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 9,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore","fan_in":1,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":38,"n_chars":1848,"n_subproofs":0,"n_tactics":24,"cyclomatic":2,"n_automation":0,"n_rewrites":0,"n_structural":9,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\",\n \"fan_in\": 1,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 38,\n \"n_chars\": 1848,\n \"n_subproofs\": 0,\n \"n_tactics\": 24,\n \"cyclomatic\": 2,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 9,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\n/-- Terminal compile-core statement lists have the same external native source\n coverage as ordinary compile-core lists. The terminal `return`/`stop` cases\n delegate their tails to the compile-core bridge exposed by the terminal\n grammar. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hTerminal :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hTerminal with\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope hRest => sorry\n | stop hRest => sorry\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n | ite hCond _hScope hThen hElse hRest ihThen ihElse => sorry\n\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\n/-- Source compile-core statement lists are covered by the recursive external\n raw-log fragment: pure bindings route through the storage/body base\n predicate, requires and terminators are direct body cases, and direct\n memory/transient writes route through the memory-write extension. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hCore with\n | nil =>\n exact .nil\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogReturn hValue) ih\n | stop _hRest ih =>\n exact .cons bridgedExternalRawLogStop ih\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n\n/-- Terminal compile-core statement lists have the same external native source\n coverage as ordinary compile-core lists. The terminal `return`/`stop` cases\n delegate their tails to the compile-core bridge exposed by the terminal\n grammar. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hTerminal :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hTerminal with\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope hRest =>\n exact .cons (bridgedExternalRawLogReturn hValue)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | stop hRest =>\n exact .cons bridgedExternalRawLogStop\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\n exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n\n"},"solution_diff":{"kind":"string","value":"@@ -273,6 +273,36 @@\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n \n+/-- Source compile-core statement lists are covered by the recursive external\n+ raw-log fragment: pure bindings route through the storage/body base\n+ predicate, requires and terminators are direct body cases, and direct\n+ memory/transient writes route through the memory-write extension. -/\n+theorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ {fields : List Field} {errors : List ErrorDef}\n+ {dynamicSource : DynamicDataSource} {scope : List String}\n+ {stmts : List Stmt}\n+ (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n+ scope stmts) :\n+ BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n+ dynamicSource stmts := by\n+ induction hCore with\n+ | nil =>\n+ exact .nil\n+ | letVar hValue _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogLetVar hValue) ih\n+ | assignVar hValue _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n+ | require_ hCond _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogRequire hCond) ih\n+ | return_ hValue _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogReturn hValue) ih\n+ | stop _hRest ih =>\n+ exact .cons bridgedExternalRawLogStop ih\n+ | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n+ | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n+\n /-- Terminal compile-core statement lists have the same external native source\n coverage as ordinary compile-core lists. The terminal `return`/`stop` cases\n delegate their tails to the compile-core bridge exposed by the terminal\n@@ -293,12 +323,21 @@\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n- | return_ hValue _hScope hRest => sorry\n- | stop hRest => sorry\n+ | return_ hValue _hScope hRest =>\n+ exact .cons (bridgedExternalRawLogReturn hValue)\n+ (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ hRest)\n+ | stop hRest =>\n+ exact .cons bridgedExternalRawLogStop\n+ (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ hRest)\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n- | ite hCond _hScope hThen hElse hRest ihThen ihElse => sorry\n+ | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\n+ exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\n+ (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ hRest)\n \n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21380,"cells":{"task_id":{"kind":"string","value":"ablate_81701029c1fb_2"},"challenge_id":{"kind":"string","value":"7bdff3781f9cde0a"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean"},"theory":{"kind":"string","value":"Safe"},"variant":{"kind":"number","value":2,"string":"2"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":6,"string":"6"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore","depth":1,"n_commands":0,"n_lines":24,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction hTerminal with\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope hRest =>\n exact .cons (bridgedExternalRawLogReturn hValue)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | stop hRest =>\n exact .cons bridgedExternalRawLogStop\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\n exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)","n_chars":1164,"n_subproofs":0,"n_tactics":24,"cyclomatic":2,"n_automation":0,"n_rewrites":0,"n_structural":9,"automation_only":false,"max_nesting":10},{"theorem_name":"bridgedSafeStmts_externalCompileCore","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n BridgedSafeStmts.externalRecursiveRawLog\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hCore)","n_chars":134,"n_subproofs":0,"n_tactics":3,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"theorem_name\": \"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 24,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction hTerminal with\\n | letVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\\n | assignVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\\n | require_ hCond _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogRequire hCond) ih\\n | return_ hValue _hScope hRest =>\\n exact .cons (bridgedExternalRawLogReturn hValue)\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\\n | stop hRest =>\\n exact .cons bridgedExternalRawLogStop\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\\n | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\\n exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\",\n \"n_chars\": 1164,\n \"n_subproofs\": 0,\n \"n_tactics\": 24,\n \"cyclomatic\": 2,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 9,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"bridgedSafeStmts_externalCompileCore\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n BridgedSafeStmts.externalRecursiveRawLog\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hCore)\",\n \"n_chars\": 134,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore","text":"/-- Source compile-core statement lists are covered by the recursive external\n raw-log fragment: pure bindings route through the storage/body base\n predicate, requires and terminators are direct body cases, and direct\n memory/transient writes route through the memory-write extension. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hCore with\n | nil =>\n exact .nil\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogReturn hValue) ih\n | stop _hRest ih =>\n exact .cons bridgedExternalRawLogStop ih\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n\n","fan_in":2,"n_lines":31,"n_chars":1499,"n_subproofs":0,"n_tactics":18,"cyclomatic":2,"n_automation":0,"n_rewrites":0,"n_structural":9,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\",\n \"text\": \"/-- Source compile-core statement lists are covered by the recursive external\\n raw-log fragment: pure bindings route through the storage/body base\\n predicate, requires and terminators are direct body cases, and direct\\n memory/transient writes route through the memory-write extension. -/\\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n {fields : List Field} {errors : List ErrorDef}\\n {dynamicSource : DynamicDataSource} {scope : List String}\\n {stmts : List Stmt}\\n (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\\n scope stmts) :\\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\\n dynamicSource stmts := by\\n induction hCore with\\n | nil =>\\n exact .nil\\n | letVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\\n | assignVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\\n | require_ hCond _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogRequire hCond) ih\\n | return_ hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogReturn hValue) ih\\n | stop _hRest ih =>\\n exact .cons bridgedExternalRawLogStop ih\\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 31,\n \"n_chars\": 1499,\n \"n_subproofs\": 0,\n \"n_tactics\": 18,\n \"cyclomatic\": 2,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 9,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"bridgedSafeStmts_externalCompileCore","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":16,"n_chars":724,"n_subproofs":0,"n_tactics":3,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"bridgedSafeStmts_externalCompileCore\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 16,\n \"n_chars\": 724,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\n/-- External source bodies accepted by the compile-core grammar are native safe\n bodies, so callers do not need to manually rebuild the raw-log recursive\n source predicate. -/\ntheorem bridgedSafeStmts_externalCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {internalRetNames : List String}\n {scope : List String} {stmts : List Stmt}\n (hCore :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts := sorry\n\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\n/-- Source compile-core statement lists are covered by the recursive external\n raw-log fragment: pure bindings route through the storage/body base\n predicate, requires and terminators are direct body cases, and direct\n memory/transient writes route through the memory-write extension. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hCore with\n | nil =>\n exact .nil\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogReturn hValue) ih\n | stop _hRest ih =>\n exact .cons bridgedExternalRawLogStop ih\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n\n/-- External source bodies accepted by the compile-core grammar are native safe\n bodies, so callers do not need to manually rebuild the raw-log recursive\n source predicate. -/\ntheorem bridgedSafeStmts_externalCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {internalRetNames : List String}\n {scope : List String} {stmts : List Stmt}\n (hCore :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts :=\n BridgedSafeStmts.externalRecursiveRawLog\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hCore)\n\n"},"solution_diff":{"kind":"string","value":"@@ -273,6 +273,36 @@\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n \n+/-- Source compile-core statement lists are covered by the recursive external\n+ raw-log fragment: pure bindings route through the storage/body base\n+ predicate, requires and terminators are direct body cases, and direct\n+ memory/transient writes route through the memory-write extension. -/\n+theorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ {fields : List Field} {errors : List ErrorDef}\n+ {dynamicSource : DynamicDataSource} {scope : List String}\n+ {stmts : List Stmt}\n+ (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n+ scope stmts) :\n+ BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n+ dynamicSource stmts := by\n+ induction hCore with\n+ | nil =>\n+ exact .nil\n+ | letVar hValue _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogLetVar hValue) ih\n+ | assignVar hValue _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n+ | require_ hCond _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogRequire hCond) ih\n+ | return_ hValue _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogReturn hValue) ih\n+ | stop _hRest ih =>\n+ exact .cons bridgedExternalRawLogStop ih\n+ | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n+ | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n+\n /-- External source bodies accepted by the compile-core grammar are native safe\n bodies, so callers do not need to manually rebuild the raw-log recursive\n source predicate. -/\n@@ -283,6 +313,9 @@\n (hCore :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n- BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts := sorry\n+ BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts :=\n+ BridgedSafeStmts.externalRecursiveRawLog\n+ (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ hCore)\n \n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21381,"cells":{"task_id":{"kind":"string","value":"ablate_81701029c1fb_3"},"challenge_id":{"kind":"string","value":"18cbde08d7ee74e3"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean"},"theory":{"kind":"string","value":"Safe"},"variant":{"kind":"number","value":3,"string":"3"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":6,"string":"6"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"bridgedSafeStmts_externalTerminalCore","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":"\n BridgedSafeStmts.externalRecursiveRawLog\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\n hTerminal)","n_chars":139,"n_subproofs":0,"n_tactics":3,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"theorem_name\": \"bridgedSafeStmts_externalTerminalCore\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \"\\n BridgedSafeStmts.externalRecursiveRawLog\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\\n hTerminal)\",\n \"n_chars\": 139,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore","text":"/-- Terminal compile-core statement lists have the same external native source\n coverage as ordinary compile-core lists. The terminal `return`/`stop` cases\n delegate their tails to the compile-core bridge exposed by the terminal\n grammar. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hTerminal :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hTerminal with\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope hRest =>\n exact .cons (bridgedExternalRawLogReturn hValue)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | stop hRest =>\n exact .cons bridgedExternalRawLogStop\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\n exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n\n","fan_in":1,"n_lines":38,"n_chars":1848,"n_subproofs":0,"n_tactics":24,"cyclomatic":2,"n_automation":0,"n_rewrites":0,"n_structural":9,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\",\n \"text\": \"/-- Terminal compile-core statement lists have the same external native source\\n coverage as ordinary compile-core lists. The terminal `return`/`stop` cases\\n delegate their tails to the compile-core bridge exposed by the terminal\\n grammar. -/\\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\\n {fields : List Field} {errors : List ErrorDef}\\n {dynamicSource : DynamicDataSource} {scope : List String}\\n {stmts : List Stmt}\\n (hTerminal :\\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\\n scope stmts) :\\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\\n dynamicSource stmts := by\\n induction hTerminal with\\n | letVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\\n | assignVar hValue _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\\n | require_ hCond _hScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogRequire hCond) ih\\n | return_ hValue _hScope hRest =>\\n exact .cons (bridgedExternalRawLogReturn hValue)\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\\n | stop hRest =>\\n exact .cons bridgedExternalRawLogStop\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\\n | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\\n exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\\n hRest)\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 38,\n \"n_chars\": 1848,\n \"n_subproofs\": 0,\n \"n_tactics\": 24,\n \"cyclomatic\": 2,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 9,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"bridgedSafeStmts_externalTerminalCore","fan_in":0,"n_deps_direct":1,"n_deps_transitive":2,"n_lines":15,"n_chars":649,"n_subproofs":0,"n_tactics":3,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":0,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"bridgedSafeStmts_externalTerminalCore\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 2,\n \"n_lines\": 15,\n \"n_chars\": 649,\n \"n_subproofs\": 0,\n \"n_tactics\": 3,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\n/-- Source compile-core statement lists are covered by the recursive external\n raw-log fragment: pure bindings route through the storage/body base\n predicate, requires and terminators are direct body cases, and direct\n memory/transient writes route through the memory-write extension. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hCore with\n | nil =>\n exact .nil\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogReturn hValue) ih\n | stop _hRest ih =>\n exact .cons bridgedExternalRawLogStop ih\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n\n/-- External source bodies accepted by the terminal-core grammar are native safe\n bodies. -/\ntheorem bridgedSafeStmts_externalTerminalCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {internalRetNames : List String}\n {scope : List String} {stmts : List Stmt}\n (hTerminal :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\n scope stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts := sorry\n\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\n/-- Source compile-core statement lists are covered by the recursive external\n raw-log fragment: pure bindings route through the storage/body base\n predicate, requires and terminators are direct body cases, and direct\n memory/transient writes route through the memory-write extension. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hCore : _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListCompileCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hCore with\n | nil =>\n exact .nil\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogReturn hValue) ih\n | stop _hRest ih =>\n exact .cons bridgedExternalRawLogStop ih\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n\n/-- Terminal compile-core statement lists have the same external native source\n coverage as ordinary compile-core lists. The terminal `return`/`stop` cases\n delegate their tails to the compile-core bridge exposed by the terminal\n grammar. -/\ntheorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {scope : List String}\n {stmts : List Stmt}\n (hTerminal :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\n scope stmts) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts := by\n induction hTerminal with\n | letVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogLetVar hValue) ih\n | assignVar hValue _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n | require_ hCond _hScope _hRest ih =>\n exact .cons (bridgedExternalRawLogRequire hCond) ih\n | return_ hValue _hScope hRest =>\n exact .cons (bridgedExternalRawLogReturn hValue)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | stop hRest =>\n exact .cons bridgedExternalRawLogStop\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\n exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n hRest)\n\n/-- External source bodies accepted by the terminal-core grammar are native safe\n bodies. -/\ntheorem bridgedSafeStmts_externalTerminalCore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {internalRetNames : List String}\n {scope : List String} {stmts : List Stmt}\n (hTerminal :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\n scope stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts :=\n BridgedSafeStmts.externalRecursiveRawLog\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\n hTerminal)\n\n"},"solution_diff":{"kind":"string","value":"@@ -303,6 +303,43 @@\n | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n \n+/-- Terminal compile-core statement lists have the same external native source\n+ coverage as ordinary compile-core lists. The terminal `return`/`stop` cases\n+ delegate their tails to the compile-core bridge exposed by the terminal\n+ grammar. -/\n+theorem bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\n+ {fields : List Field} {errors : List ErrorDef}\n+ {dynamicSource : DynamicDataSource} {scope : List String}\n+ {stmts : List Stmt}\n+ (hTerminal :\n+ _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\n+ scope stmts) :\n+ BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n+ dynamicSource stmts := by\n+ induction hTerminal with\n+ | letVar hValue _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogLetVar hValue) ih\n+ | assignVar hValue _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogAssignVar hValue) ih\n+ | require_ hCond _hScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogRequire hCond) ih\n+ | return_ hValue _hScope hRest =>\n+ exact .cons (bridgedExternalRawLogReturn hValue)\n+ (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ hRest)\n+ | stop hRest =>\n+ exact .cons bridgedExternalRawLogStop\n+ (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ hRest)\n+ | mstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogMstore hOffset hValue) ih\n+ | tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>\n+ exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih\n+ | ite hCond _hScope hThen hElse hRest ihThen ihElse =>\n+ exact .cons (bridgedExternalRawLogIte hCond ihThen ihElse)\n+ (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore\n+ hRest)\n+\n /-- External source bodies accepted by the terminal-core grammar are native safe\n bodies. -/\n theorem bridgedSafeStmts_externalTerminalCore\n@@ -312,6 +349,9 @@\n (hTerminal :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.StmtListTerminalCore\n scope stmts) :\n- BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts := sorry\n+ BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts :=\n+ BridgedSafeStmts.externalRecursiveRawLog\n+ (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore\n+ hTerminal)\n \n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21382,"cells":{"task_id":{"kind":"string","value":"ablate_81701029c1fb_4"},"challenge_id":{"kind":"string","value":"9321d0d544957037"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean"},"theory":{"kind":"string","value":"Safe"},"variant":{"kind":"number","value":4,"string":"4"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":6,"string":"6"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"BridgedSafeStmts.toBridgedSource","depth":1,"n_commands":0,"n_lines":88,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction hSafe with\n | externalRecursiveRawLog hStmts =>\n exact fun stmt hMem => .externalRecursiveRawLog\n (mem_of_externalRecursiveRawLogStmts _ hStmts stmt hMem)\n | internalRecursiveRawLog hStmts =>\n exact fun stmt hMem => .internalRecursiveRawLog\n (mem_of_internalRecursiveRawLogStmts _ hStmts stmt hMem)\n | storage hStmts =>\n exact fun stmt hMem => .storage (hStmts stmt hMem)\n | storageAddr hStmts =>\n exact fun stmt hMem => .storageAddr (hStmts stmt hMem)\n | require hStmts =>\n exact fun stmt hMem => .require (hStmts stmt hMem)\n | setStorageArrayElement hStmts =>\n exact fun stmt hMem => .setStorageArrayElement (hStmts stmt hMem)\n | mappingChain hStmts =>\n exact fun stmt hMem => .mappingChain (hStmts stmt hMem)\n | mappingWrite hStmts =>\n exact fun stmt hMem => .mappingWrite (hStmts stmt hMem)\n | mappingWriteMultiSlot hStmts =>\n exact fun stmt hMem => .mappingWriteMultiSlot (hStmts stmt hMem)\n | mappingWrite2 hStmts =>\n exact fun stmt hMem => .mappingWrite2 (hStmts stmt hMem)\n | mappingWrite2MultiSlot hStmts =>\n exact fun stmt hMem => .mappingWrite2MultiSlot (hStmts stmt hMem)\n | structMember hStmts =>\n exact fun stmt hMem => .structMember (hStmts stmt hMem)\n | structMember2 hStmts =>\n exact fun stmt hMem => .structMember2 (hStmts stmt hMem)\n | structMemberNonzero hStmts =>\n exact fun stmt hMem => .structMemberNonzero (hStmts stmt hMem)\n | structMember2Nonzero hStmts =>\n exact fun stmt hMem => .structMember2Nonzero (hStmts stmt hMem)\n | structMemberMultiSlot hStmts =>\n exact fun stmt hMem => .structMemberMultiSlot (hStmts stmt hMem)\n | structMember2MultiSlot hStmts =>\n exact fun stmt hMem => .structMember2MultiSlot (hStmts stmt hMem)\n | mappingWord hStmts =>\n exact fun stmt hMem => .mappingWord (hStmts stmt hMem)\n | mapping2Word hStmts =>\n exact fun stmt hMem => .mapping2Word (hStmts stmt hMem)\n | mappingWordNonzero hStmts =>\n exact fun stmt hMem => .mappingWordNonzero (hStmts stmt hMem)\n | mapping2WordNonzero hStmts =>\n exact fun stmt hMem => .mapping2WordNonzero (hStmts stmt hMem)\n | mappingWordMultiSlot hStmts =>\n exact fun stmt hMem => .mappingWordMultiSlot (hStmts stmt hMem)\n | mapping2WordMultiSlot hStmts =>\n exact fun stmt hMem => .mapping2WordMultiSlot (hStmts stmt hMem)\n | mappingWordMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .mappingWordMultiSlotNonzero (hStmts stmt hMem)\n | mapping2WordMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .mapping2WordMultiSlotNonzero (hStmts stmt hMem)\n | structMemberMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .structMemberMultiSlotNonzero (hStmts stmt hMem)\n | structMember2MultiSlotNonzero hStmts =>\n exact fun stmt hMem => .structMember2MultiSlotNonzero (hStmts stmt hMem)\n | mappingPackedWord hStmts =>\n exact fun stmt hMem => .mappingPackedWord (hStmts stmt hMem)\n | mappingPackedWordNonzero hStmts =>\n exact fun stmt hMem => .mappingPackedWordNonzero (hStmts stmt hMem)\n | mappingPackedWordMultiSlot hStmts =>\n exact fun stmt hMem => .mappingPackedWordMultiSlot (hStmts stmt hMem)\n | mappingPackedWordMultiSlotNonzero hStmts =>\n exact fun stmt hMem =>\n .mappingPackedWordMultiSlotNonzero (hStmts stmt hMem)\n | returnValuesExternal hStmts =>\n exact fun stmt hMem => .returnValuesExternal (hStmts stmt hMem)\n | returnValuesInternal hStmts =>\n exact fun stmt hMem => .returnValuesInternal (hStmts stmt hMem)\n | mstore hStmts =>\n exact fun stmt hMem => .mstore (hStmts stmt hMem)\n | tstore hStmts =>\n exact fun stmt hMem => .tstore (hStmts stmt hMem)\n | storageArrayPush hStmts =>\n exact fun stmt hMem => .storageArrayPush (hStmts stmt hMem)\n | storageArrayPop hStmts =>\n exact fun stmt hMem => .storageArrayPop (hStmts stmt hMem)\n | internalCall hStmts =>\n exact fun stmt hMem => .internalCall (hStmts stmt hMem)\n | externalCallBind hStmts =>\n exact fun stmt hMem => .externalCallBind (hStmts stmt hMem)\n | append _ _ ihPfx ihSfx =>\n intro stmt hMem\n rcases List.mem_append.mp hMem with h | h\n · exact ihPfx stmt h\n · exact ihSfx stmt h","n_chars":4225,"n_subproofs":0,"n_tactics":88,"cyclomatic":3,"n_automation":0,"n_rewrites":0,"n_structural":44,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"BridgedSafeStmts.toBridgedSource\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 88,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction hSafe with\\n | externalRecursiveRawLog hStmts =>\\n exact fun stmt hMem => .externalRecursiveRawLog\\n (mem_of_externalRecursiveRawLogStmts _ hStmts stmt hMem)\\n | internalRecursiveRawLog hStmts =>\\n exact fun stmt hMem => .internalRecursiveRawLog\\n (mem_of_internalRecursiveRawLogStmts _ hStmts stmt hMem)\\n | storage hStmts =>\\n exact fun stmt hMem => .storage (hStmts stmt hMem)\\n | storageAddr hStmts =>\\n exact fun stmt hMem => .storageAddr (hStmts stmt hMem)\\n | require hStmts =>\\n exact fun stmt hMem => .require (hStmts stmt hMem)\\n | setStorageArrayElement hStmts =>\\n exact fun stmt hMem => .setStorageArrayElement (hStmts stmt hMem)\\n | mappingChain hStmts =>\\n exact fun stmt hMem => .mappingChain (hStmts stmt hMem)\\n | mappingWrite hStmts =>\\n exact fun stmt hMem => .mappingWrite (hStmts stmt hMem)\\n | mappingWriteMultiSlot hStmts =>\\n exact fun stmt hMem => .mappingWriteMultiSlot (hStmts stmt hMem)\\n | mappingWrite2 hStmts =>\\n exact fun stmt hMem => .mappingWrite2 (hStmts stmt hMem)\\n | mappingWrite2MultiSlot hStmts =>\\n exact fun stmt hMem => .mappingWrite2MultiSlot (hStmts stmt hMem)\\n | structMember hStmts =>\\n exact fun stmt hMem => .structMember (hStmts stmt hMem)\\n | structMember2 hStmts =>\\n exact fun stmt hMem => .structMember2 (hStmts stmt hMem)\\n | structMemberNonzero hStmts =>\\n exact fun stmt hMem => .structMemberNonzero (hStmts stmt hMem)\\n | structMember2Nonzero hStmts =>\\n exact fun stmt hMem => .structMember2Nonzero (hStmts stmt hMem)\\n | structMemberMultiSlot hStmts =>\\n exact fun stmt hMem => .structMemberMultiSlot (hStmts stmt hMem)\\n | structMember2MultiSlot hStmts =>\\n exact fun stmt hMem => .structMember2MultiSlot (hStmts stmt hMem)\\n | mappingWord hStmts =>\\n exact fun stmt hMem => .mappingWord (hStmts stmt hMem)\\n | mapping2Word hStmts =>\\n exact fun stmt hMem => .mapping2Word (hStmts stmt hMem)\\n | mappingWordNonzero hStmts =>\\n exact fun stmt hMem => .mappingWordNonzero (hStmts stmt hMem)\\n | mapping2WordNonzero hStmts =>\\n exact fun stmt hMem => .mapping2WordNonzero (hStmts stmt hMem)\\n | mappingWordMultiSlot hStmts =>\\n exact fun stmt hMem => .mappingWordMultiSlot (hStmts stmt hMem)\\n | mapping2WordMultiSlot hStmts =>\\n exact fun stmt hMem => .mapping2WordMultiSlot (hStmts stmt hMem)\\n | mappingWordMultiSlotNonzero hStmts =>\\n exact fun stmt hMem => .mappingWordMultiSlotNonzero (hStmts stmt hMem)\\n | mapping2WordMultiSlotNonzero hStmts =>\\n exact fun stmt hMem => .mapping2WordMultiSlotNonzero (hStmts stmt hMem)\\n | structMemberMultiSlotNonzero hStmts =>\\n exact fun stmt hMem => .structMemberMultiSlotNonzero (hStmts stmt hMem)\\n | structMember2MultiSlotNonzero hStmts =>\\n exact fun stmt hMem => .structMember2MultiSlotNonzero (hStmts stmt hMem)\\n | mappingPackedWord hStmts =>\\n exact fun stmt hMem => .mappingPackedWord (hStmts stmt hMem)\\n | mappingPackedWordNonzero hStmts =>\\n exact fun stmt hMem => .mappingPackedWordNonzero (hStmts stmt hMem)\\n | mappingPackedWordMultiSlot hStmts =>\\n exact fun stmt hMem => .mappingPackedWordMultiSlot (hStmts stmt hMem)\\n | mappingPackedWordMultiSlotNonzero hStmts =>\\n exact fun stmt hMem =>\\n .mappingPackedWordMultiSlotNonzero (hStmts stmt hMem)\\n | returnValuesExternal hStmts =>\\n exact fun stmt hMem => .returnValuesExternal (hStmts stmt hMem)\\n | returnValuesInternal hStmts =>\\n exact fun stmt hMem => .returnValuesInternal (hStmts stmt hMem)\\n | mstore hStmts =>\\n exact fun stmt hMem => .mstore (hStmts stmt hMem)\\n | tstore hStmts =>\\n exact fun stmt hMem => .tstore (hStmts stmt hMem)\\n | storageArrayPush hStmts =>\\n exact fun stmt hMem => .storageArrayPush (hStmts stmt hMem)\\n | storageArrayPop hStmts =>\\n exact fun stmt hMem => .storageArrayPop (hStmts stmt hMem)\\n | internalCall hStmts =>\\n exact fun stmt hMem => .internalCall (hStmts stmt hMem)\\n | externalCallBind hStmts =>\\n exact fun stmt hMem => .externalCallBind (hStmts stmt hMem)\\n | append _ _ ihPfx ihSfx =>\\n intro stmt hMem\\n rcases List.mem_append.mp hMem with h | h\\n · exact ihPfx stmt h\\n · exact ihSfx stmt h\",\n \"n_chars\": 4225,\n \"n_subproofs\": 0,\n \"n_tactics\": 88,\n \"cyclomatic\": 3,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 44,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"mem_of_internalRecursiveRawLogStmts","text":"private theorem mem_of_internalRecursiveRawLogStmts\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n ∀ (stmts : List Stmt),\n BridgedSourceInternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts →\n ∀ stmt ∈ stmts,\n BridgedSourceInternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource stmt := by\n intro stmts\n induction stmts with\n | nil => intro _ stmt hMem; cases hMem\n | cons head tail ih =>\n intro hStmts stmt hMem\n cases hStmts with\n | cons hHead hTail =>\n cases hMem with\n | head => exact hHead\n | tail _ hMem => exact ih hTail stmt hMem\n\n","fan_in":1,"n_lines":21,"n_chars":703,"n_subproofs":0,"n_tactics":12,"cyclomatic":5,"n_automation":0,"n_rewrites":0,"n_structural":9,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"mem_of_internalRecursiveRawLogStmts\",\n \"text\": \"private theorem mem_of_internalRecursiveRawLogStmts\\n {fields : List Field} {errors : List ErrorDef}\\n {dynamicSource : DynamicDataSource} :\\n ∀ (stmts : List Stmt),\\n BridgedSourceInternalRecursiveBodyWithRawLogStmts fields errors\\n dynamicSource stmts →\\n ∀ stmt ∈ stmts,\\n BridgedSourceInternalRecursiveBodyWithRawLogStmt fields errors\\n dynamicSource stmt := by\\n intro stmts\\n induction stmts with\\n | nil => intro _ stmt hMem; cases hMem\\n | cons head tail ih =>\\n intro hStmts stmt hMem\\n cases hStmts with\\n | cons hHead hTail =>\\n cases hMem with\\n | head => exact hHead\\n | tail _ hMem => exact ih hTail stmt hMem\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 21,\n \"n_chars\": 703,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 5,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 9,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"BridgedSafeStmts.toBridgedSource","fan_in":2,"n_deps_direct":2,"n_deps_transitive":2,"n_lines":103,"n_chars":4965,"n_subproofs":0,"n_tactics":88,"cyclomatic":3,"n_automation":0,"n_rewrites":0,"n_structural":44,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"BridgedSafeStmts.toBridgedSource\",\n \"fan_in\": 2,\n \"n_deps_direct\": 2,\n \"n_deps_transitive\": 2,\n \"n_lines\": 103,\n \"n_chars\": 4965,\n \"n_subproofs\": 0,\n \"n_tactics\": 88,\n \"cyclomatic\": 3,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 44,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\nprivate theorem mem_of_externalRecursiveRawLogStmts\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n ∀ (stmts : List Stmt),\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts →\n ∀ stmt ∈ stmts,\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource stmt := by\n intro stmts\n induction stmts with\n | nil => intro _ stmt hMem; cases hMem\n | cons head tail ih =>\n intro hStmts stmt hMem\n cases hStmts with\n | cons hHead hTail =>\n cases hMem with\n | head => exact hHead\n | tail _ hMem => exact ih hTail stmt hMem\n\n/-- Every list-level whitelist witness flattens to the per-statement union:\na `BridgedSafeStmts` list is pointwise `BridgedSourceStmt`. Pointwise\nfragment arms forward their member hypothesis; the two recursive raw-log\narms extract members from their list inductives; `append` splits on\n`List.mem_append`. -/\ntheorem BridgedSafeStmts.toBridgedSource\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {internalRetNames : List String}\n {isInternal : Bool} {stmts : List Stmt}\n (hSafe : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal stmts) :\n ∀ stmt ∈ stmts,\n BridgedSourceStmt fields errors dynamicSource internalRetNames\n isInternal stmt := by\n induction hSafe with\n | externalRecursiveRawLog hStmts =>\n exact fun stmt hMem => .externalRecursiveRawLog\n (mem_of_externalRecursiveRawLogStmts _ hStmts stmt hMem)\n | internalRecursiveRawLog hStmts => sorry\n | storage hStmts =>\n exact fun stmt hMem => .storage (hStmts stmt hMem)\n | storageAddr hStmts =>\n exact fun stmt hMem => .storageAddr (hStmts stmt hMem)\n | require hStmts =>\n exact fun stmt hMem => .require (hStmts stmt hMem)\n | setStorageArrayElement hStmts =>\n exact fun stmt hMem => .setStorageArrayElement (hStmts stmt hMem)\n | mappingChain hStmts =>\n exact fun stmt hMem => .mappingChain (hStmts stmt hMem)\n | mappingWrite hStmts =>\n exact fun stmt hMem => .mappingWrite (hStmts stmt hMem)\n | mappingWriteMultiSlot hStmts =>\n exact fun stmt hMem => .mappingWriteMultiSlot (hStmts stmt hMem)\n | mappingWrite2 hStmts =>\n exact fun stmt hMem => .mappingWrite2 (hStmts stmt hMem)\n | mappingWrite2MultiSlot hStmts =>\n exact fun stmt hMem => .mappingWrite2MultiSlot (hStmts stmt hMem)\n | structMember hStmts =>\n exact fun stmt hMem => .structMember (hStmts stmt hMem)\n | structMember2 hStmts =>\n exact fun stmt hMem => .structMember2 (hStmts stmt hMem)\n | structMemberNonzero hStmts =>\n exact fun stmt hMem => .structMemberNonzero (hStmts stmt hMem)\n | structMember2Nonzero hStmts =>\n exact fun stmt hMem => .structMember2Nonzero (hStmts stmt hMem)\n | structMemberMultiSlot hStmts =>\n exact fun stmt hMem => .structMemberMultiSlot (hStmts stmt hMem)\n | structMember2MultiSlot hStmts =>\n exact fun stmt hMem => .structMember2MultiSlot (hStmts stmt hMem)\n | mappingWord hStmts =>\n exact fun stmt hMem => .mappingWord (hStmts stmt hMem)\n | mapping2Word hStmts =>\n exact fun stmt hMem => .mapping2Word (hStmts stmt hMem)\n | mappingWordNonzero hStmts =>\n exact fun stmt hMem => .mappingWordNonzero (hStmts stmt hMem)\n | mapping2WordNonzero hStmts =>\n exact fun stmt hMem => .mapping2WordNonzero (hStmts stmt hMem)\n | mappingWordMultiSlot hStmts =>\n exact fun stmt hMem => .mappingWordMultiSlot (hStmts stmt hMem)\n | mapping2WordMultiSlot hStmts =>\n exact fun stmt hMem => .mapping2WordMultiSlot (hStmts stmt hMem)\n | mappingWordMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .mappingWordMultiSlotNonzero (hStmts stmt hMem)\n | mapping2WordMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .mapping2WordMultiSlotNonzero (hStmts stmt hMem)\n | structMemberMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .structMemberMultiSlotNonzero (hStmts stmt hMem)\n | structMember2MultiSlotNonzero hStmts =>\n exact fun stmt hMem => .structMember2MultiSlotNonzero (hStmts stmt hMem)\n | mappingPackedWord hStmts =>\n exact fun stmt hMem => .mappingPackedWord (hStmts stmt hMem)\n | mappingPackedWordNonzero hStmts =>\n exact fun stmt hMem => .mappingPackedWordNonzero (hStmts stmt hMem)\n | mappingPackedWordMultiSlot hStmts =>\n exact fun stmt hMem => .mappingPackedWordMultiSlot (hStmts stmt hMem)\n | mappingPackedWordMultiSlotNonzero hStmts =>\n exact fun stmt hMem =>\n .mappingPackedWordMultiSlotNonzero (hStmts stmt hMem)\n | returnValuesExternal hStmts =>\n exact fun stmt hMem => .returnValuesExternal (hStmts stmt hMem)\n | returnValuesInternal hStmts =>\n exact fun stmt hMem => .returnValuesInternal (hStmts stmt hMem)\n | mstore hStmts =>\n exact fun stmt hMem => .mstore (hStmts stmt hMem)\n | tstore hStmts =>\n exact fun stmt hMem => .tstore (hStmts stmt hMem)\n | storageArrayPush hStmts =>\n exact fun stmt hMem => .storageArrayPush (hStmts stmt hMem)\n | storageArrayPop hStmts =>\n exact fun stmt hMem => .storageArrayPop (hStmts stmt hMem)\n | internalCall hStmts =>\n exact fun stmt hMem => .internalCall (hStmts stmt hMem)\n | externalCallBind hStmts =>\n exact fun stmt hMem => .externalCallBind (hStmts stmt hMem)\n | append _ _ ihPfx ihSfx =>\n intro stmt hMem\n rcases List.mem_append.mp hMem with h | h\n · exact ihPfx stmt h\n · exact ihSfx stmt h\n\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base\nimport Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic\n\nset_option linter.unusedSimpArgs false\n\nnamespace Compiler.Proofs.YulGeneration.Backends\n\nopen Compiler\nopen Compiler.Yul\nopen Compiler.CompilationModel\nopen Compiler.Proofs.YulGeneration\nopen Verity.Core.Free\n\n/-!\n## Universal safe-body closure\n\n`BridgedSafeStmts` is the source-level whitelist used by the EVMYulLean native\nlowering report: it collects the statement-list fragments that this module has\nproved to compile into `BridgedStmts`. Internal helper calls and typed external\ncall binds are admitted through an explicit `BridgedFunctionTable` witness,\nwhich proves the called Yul functions resolve to bridged bodies. Opaque ECM\nstatements remain outside this universal whitelist until concrete modules\nprovide bridgeable-output obligations.\n-/\n\ninductive BridgedSafeStmts\n (fields : List Field) (errors : List ErrorDef)\n (dynamicSource : DynamicDataSource) (internalRetNames : List String) :\n Bool → List Stmt → Prop\n | externalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceExternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | internalRecursiveRawLog {stmts : List Stmt}\n (hStmts : BridgedSourceInternalRecursiveBodyWithRawLogStmts\n fields errors dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | storage {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageAddr {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageAddrStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | require {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceRequireStmts fields dynamicSource stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | setStorageArrayElement {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceSetStorageArrayElementStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingChain {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingChainStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWriteMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWriteMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWrite2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWrite2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2 {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2Stmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2Nonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2NonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2Word {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mapping2WordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMapping2WordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMemberMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMemberMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | structMember2MultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStructMember2MultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWord {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlot {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | mappingPackedWordMultiSlotNonzero {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMappingPackedWordMultiSlotNonzeroStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | returnValuesExternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesExternalStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames false stmts\n | returnValuesInternal {stmts : List Stmt}\n (hStmts : BridgedSourceReturnValuesInternalStmts internalRetNames stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames true stmts\n | mstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceMstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | tstore {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceTstoreStmts stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPush {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPushStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | storageArrayPop {isInternal : Bool} {stmts : List Stmt}\n (hStmts : BridgedSourceStorageArrayPopStmts fields stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | internalCall {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceInternalCallStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | externalCallBind {isInternal : Bool} {stmts : List Stmt}\n {table : BridgedFunctionTable}\n (hStmts : BridgedSourceExternalCallBindStmts table stmts) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal stmts\n | append {isInternal : Bool} {pfx sfx : List Stmt}\n (hPfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal pfx)\n (hSfx : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal sfx) :\n BridgedSafeStmts fields errors dynamicSource internalRetNames isInternal\n (pfx ++ sfx)\n\n/-- A `let` binding whose RHS is syntactic `keccak256(offset, size)` is a\n native pure-binding source statement when the offset and size arguments are\n compile-core expressions. This deliberately stays outside\n `StmtListCompileCore`, whose source/IR semantic theorem still excludes\n memory-slice hashing. -/\ntheorem bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore\n {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourcePureBindingStmt\n (.letVar name (.keccak256 offset size)) :=\n BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)\n (bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)\n\nprivate def bridgedExternalRawLogLetVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.letVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogLetKeccak\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {offset size : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hSize :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore size) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.letVar name (.keccak256 offset size)) :=\n .base (.base (.base (.storage (.pureBinding\n (bridgedSourcePureBindingStmt_letKeccak_of_exprCompileCore hOffset hSize)))))\n\nprivate def bridgedExternalRawLogAssignVar\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {name : String} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.assignVar name value) :=\n .base (.base (.base (.storage (.pureBinding\n (.assignVar _ _ (bridgedSourceExpr_of_exprCompileCore hValue))))))\n\nprivate def bridgedExternalRawLogRequire\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {cond : Expr} {message : String}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.require cond message) :=\n .base (.base (.base (.require\n (bridgedSourceRequireStmt_of_exprCompileCore hCond))))\n\nprivate def bridgedExternalRawLogReturn\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {value : Expr}\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.return value) :=\n .base (.base (.base (.terminator\n (.returnExternal _ (bridgedSourceExpr_of_exprCompileCore hValue)))))\n\nprivate def bridgedExternalRawLogStop\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource .stop :=\n .base (.base (.base (.terminator .stop)))\n\nprivate def bridgedExternalRawLogMstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.mstore offset value) :=\n .base (.base (.memoryWrite\n (.mstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogTstore\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {offset value : Expr}\n (hOffset :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore offset)\n (hValue :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore value) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.tstore offset value) :=\n .base (.base (.memoryWrite\n (.tstore _ _ (bridgedSourceExpr_of_exprCompileCore hOffset)\n (bridgedSourceExpr_of_exprCompileCore hValue))))\n\nprivate def bridgedExternalRawLogIte\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource}\n {cond : Expr} {thenBranch elseBranch : List Stmt}\n (hCond :\n _root_.Compiler.Proofs.IRGeneration.FunctionBody.ExprCompileCore cond)\n (hThen :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource thenBranch)\n (hElse :\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource elseBranch) :\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource (.ite cond thenBranch elseBranch) :=\n .ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse\n\nprivate theorem mem_of_externalRecursiveRawLogStmts\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n ∀ (stmts : List Stmt),\n BridgedSourceExternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts →\n ∀ stmt ∈ stmts,\n BridgedSourceExternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource stmt := by\n intro stmts\n induction stmts with\n | nil => intro _ stmt hMem; cases hMem\n | cons head tail ih =>\n intro hStmts stmt hMem\n cases hStmts with\n | cons hHead hTail =>\n cases hMem with\n | head => exact hHead\n | tail _ hMem => exact ih hTail stmt hMem\n\nprivate theorem mem_of_internalRecursiveRawLogStmts\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n ∀ (stmts : List Stmt),\n BridgedSourceInternalRecursiveBodyWithRawLogStmts fields errors\n dynamicSource stmts →\n ∀ stmt ∈ stmts,\n BridgedSourceInternalRecursiveBodyWithRawLogStmt fields errors\n dynamicSource stmt := by\n intro stmts\n induction stmts with\n | nil => intro _ stmt hMem; cases hMem\n | cons head tail ih =>\n intro hStmts stmt hMem\n cases hStmts with\n | cons hHead hTail =>\n cases hMem with\n | head => exact hHead\n | tail _ hMem => exact ih hTail stmt hMem\n\n/-- Every list-level whitelist witness flattens to the per-statement union:\na `BridgedSafeStmts` list is pointwise `BridgedSourceStmt`. Pointwise\nfragment arms forward their member hypothesis; the two recursive raw-log\narms extract members from their list inductives; `append` splits on\n`List.mem_append`. -/\ntheorem BridgedSafeStmts.toBridgedSource\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} {internalRetNames : List String}\n {isInternal : Bool} {stmts : List Stmt}\n (hSafe : BridgedSafeStmts fields errors dynamicSource internalRetNames\n isInternal stmts) :\n ∀ stmt ∈ stmts,\n BridgedSourceStmt fields errors dynamicSource internalRetNames\n isInternal stmt := by\n induction hSafe with\n | externalRecursiveRawLog hStmts =>\n exact fun stmt hMem => .externalRecursiveRawLog\n (mem_of_externalRecursiveRawLogStmts _ hStmts stmt hMem)\n | internalRecursiveRawLog hStmts =>\n exact fun stmt hMem => .internalRecursiveRawLog\n (mem_of_internalRecursiveRawLogStmts _ hStmts stmt hMem)\n | storage hStmts =>\n exact fun stmt hMem => .storage (hStmts stmt hMem)\n | storageAddr hStmts =>\n exact fun stmt hMem => .storageAddr (hStmts stmt hMem)\n | require hStmts =>\n exact fun stmt hMem => .require (hStmts stmt hMem)\n | setStorageArrayElement hStmts =>\n exact fun stmt hMem => .setStorageArrayElement (hStmts stmt hMem)\n | mappingChain hStmts =>\n exact fun stmt hMem => .mappingChain (hStmts stmt hMem)\n | mappingWrite hStmts =>\n exact fun stmt hMem => .mappingWrite (hStmts stmt hMem)\n | mappingWriteMultiSlot hStmts =>\n exact fun stmt hMem => .mappingWriteMultiSlot (hStmts stmt hMem)\n | mappingWrite2 hStmts =>\n exact fun stmt hMem => .mappingWrite2 (hStmts stmt hMem)\n | mappingWrite2MultiSlot hStmts =>\n exact fun stmt hMem => .mappingWrite2MultiSlot (hStmts stmt hMem)\n | structMember hStmts =>\n exact fun stmt hMem => .structMember (hStmts stmt hMem)\n | structMember2 hStmts =>\n exact fun stmt hMem => .structMember2 (hStmts stmt hMem)\n | structMemberNonzero hStmts =>\n exact fun stmt hMem => .structMemberNonzero (hStmts stmt hMem)\n | structMember2Nonzero hStmts =>\n exact fun stmt hMem => .structMember2Nonzero (hStmts stmt hMem)\n | structMemberMultiSlot hStmts =>\n exact fun stmt hMem => .structMemberMultiSlot (hStmts stmt hMem)\n | structMember2MultiSlot hStmts =>\n exact fun stmt hMem => .structMember2MultiSlot (hStmts stmt hMem)\n | mappingWord hStmts =>\n exact fun stmt hMem => .mappingWord (hStmts stmt hMem)\n | mapping2Word hStmts =>\n exact fun stmt hMem => .mapping2Word (hStmts stmt hMem)\n | mappingWordNonzero hStmts =>\n exact fun stmt hMem => .mappingWordNonzero (hStmts stmt hMem)\n | mapping2WordNonzero hStmts =>\n exact fun stmt hMem => .mapping2WordNonzero (hStmts stmt hMem)\n | mappingWordMultiSlot hStmts =>\n exact fun stmt hMem => .mappingWordMultiSlot (hStmts stmt hMem)\n | mapping2WordMultiSlot hStmts =>\n exact fun stmt hMem => .mapping2WordMultiSlot (hStmts stmt hMem)\n | mappingWordMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .mappingWordMultiSlotNonzero (hStmts stmt hMem)\n | mapping2WordMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .mapping2WordMultiSlotNonzero (hStmts stmt hMem)\n | structMemberMultiSlotNonzero hStmts =>\n exact fun stmt hMem => .structMemberMultiSlotNonzero (hStmts stmt hMem)\n | structMember2MultiSlotNonzero hStmts =>\n exact fun stmt hMem => .structMember2MultiSlotNonzero (hStmts stmt hMem)\n | mappingPackedWord hStmts =>\n exact fun stmt hMem => .mappingPackedWord (hStmts stmt hMem)\n | mappingPackedWordNonzero hStmts =>\n exact fun stmt hMem => .mappingPackedWordNonzero (hStmts stmt hMem)\n | mappingPackedWordMultiSlot hStmts =>\n exact fun stmt hMem => .mappingPackedWordMultiSlot (hStmts stmt hMem)\n | mappingPackedWordMultiSlotNonzero hStmts =>\n exact fun stmt hMem =>\n .mappingPackedWordMultiSlotNonzero (hStmts stmt hMem)\n | returnValuesExternal hStmts =>\n exact fun stmt hMem => .returnValuesExternal (hStmts stmt hMem)\n | returnValuesInternal hStmts =>\n exact fun stmt hMem => .returnValuesInternal (hStmts stmt hMem)\n | mstore hStmts =>\n exact fun stmt hMem => .mstore (hStmts stmt hMem)\n | tstore hStmts =>\n exact fun stmt hMem => .tstore (hStmts stmt hMem)\n | storageArrayPush hStmts =>\n exact fun stmt hMem => .storageArrayPush (hStmts stmt hMem)\n | storageArrayPop hStmts =>\n exact fun stmt hMem => .storageArrayPop (hStmts stmt hMem)\n | internalCall hStmts =>\n exact fun stmt hMem => .internalCall (hStmts stmt hMem)\n | externalCallBind hStmts =>\n exact fun stmt hMem => .externalCallBind (hStmts stmt hMem)\n | append _ _ ihPfx ihSfx =>\n intro stmt hMem\n rcases List.mem_append.mp hMem with h | h\n · exact ihPfx stmt h\n · exact ihSfx stmt h\n\n"},"solution_diff":{"kind":"string","value":"@@ -293,6 +293,26 @@\n | head => exact hHead\n | tail _ hMem => exact ih hTail stmt hMem\n \n+private theorem mem_of_internalRecursiveRawLogStmts\n+ {fields : List Field} {errors : List ErrorDef}\n+ {dynamicSource : DynamicDataSource} :\n+ ∀ (stmts : List Stmt),\n+ BridgedSourceInternalRecursiveBodyWithRawLogStmts fields errors\n+ dynamicSource stmts →\n+ ∀ stmt ∈ stmts,\n+ BridgedSourceInternalRecursiveBodyWithRawLogStmt fields errors\n+ dynamicSource stmt := by\n+ intro stmts\n+ induction stmts with\n+ | nil => intro _ stmt hMem; cases hMem\n+ | cons head tail ih =>\n+ intro hStmts stmt hMem\n+ cases hStmts with\n+ | cons hHead hTail =>\n+ cases hMem with\n+ | head => exact hHead\n+ | tail _ hMem => exact ih hTail stmt hMem\n+\n /-- Every list-level whitelist witness flattens to the per-statement union:\n a `BridgedSafeStmts` list is pointwise `BridgedSourceStmt`. Pointwise\n fragment arms forward their member hypothesis; the two recursive raw-log\n@@ -311,7 +331,9 @@\n | externalRecursiveRawLog hStmts =>\n exact fun stmt hMem => .externalRecursiveRawLog\n (mem_of_externalRecursiveRawLogStmts _ hStmts stmt hMem)\n- | internalRecursiveRawLog hStmts => sorry\n+ | internalRecursiveRawLog hStmts =>\n+ exact fun stmt hMem => .internalRecursiveRawLog\n+ (mem_of_internalRecursiveRawLogStmts _ hStmts stmt hMem)\n | storage hStmts =>\n exact fun stmt hMem => .storage (hStmts stmt hMem)\n | storageAddr hStmts =>\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21383,"cells":{"task_id":{"kind":"string","value":"ablate_bc040358e506_0"},"challenge_id":{"kind":"string","value":"856e1b61aeb1017e"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Contracts/Smoke/EIP712StaticSmoke.lean"},"theory":{"kind":"string","value":"EIP712StaticSmoke"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":1,"string":"1"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"permitStaticHash_eip712Supported_and_digest_correct","depth":1,"n_commands":0,"n_lines":11,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n constructor\n · exact permitStaticHashAndDigest_supported\n · constructor\n · constructor\n · rfl\n · exact Compiler.Modules.Hashing.abiEncodeStaticWordsModule_compile_permitStructHash_layout\n permitTypeHash\n · constructor\n · rfl\n · exact Compiler.Modules.Hashing.eip712DigestModule_compile_digest_layout","n_chars":350,"n_subproofs":0,"n_tactics":11,"cyclomatic":5,"n_automation":2,"n_rewrites":0,"n_structural":7,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"permitStaticHash_eip712Supported_and_digest_correct\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 11,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n constructor\\n · exact permitStaticHashAndDigest_supported\\n · constructor\\n · constructor\\n · rfl\\n · exact Compiler.Modules.Hashing.abiEncodeStaticWordsModule_compile_permitStructHash_layout\\n permitTypeHash\\n · constructor\\n · rfl\\n · exact Compiler.Modules.Hashing.eip712DigestModule_compile_digest_layout\",\n \"n_chars\": 350,\n \"n_subproofs\": 0,\n \"n_tactics\": 11,\n \"cyclomatic\": 5,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 7,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"permitStaticHashAndDigest_supported","text":"private theorem permitStaticHashAndDigest_supported :\n SupportedStmtList [] permitScope permitStaticHashAndDigestStmts := by\n change SupportedStmtList [] permitScope ([permitStructHashStmt] ++ [permitDigestStmt])\n apply SupportedStmtList.append\n · apply SupportedStmtList.pureHashingEcm\n · simp [ecmPureHashing, Compiler.Modules.Hashing.abiEncodeStaticWordsModule]\n · intro a ha\n simp at ha\n rcases ha with rfl | rfl | rfl | rfl | rfl | rfl <;> constructor\n · intro a ha\n simp at ha\n rcases ha with rfl | rfl | rfl | rfl | rfl | rfl <;>\n simp [FunctionBody.exprBoundNamesInScope, FunctionBody.exprBoundNames, permitScope]\n · apply SupportedStmtList.pureHashingEcm\n · simp [ecmPureHashing, Compiler.Modules.Hashing.eip712DigestModule]\n · intro a ha\n simp at ha\n rcases ha with rfl | rfl <;> constructor\n · intro a ha\n simp at ha\n rcases ha with rfl | rfl <;>\n simp [FunctionBody.exprBoundNamesInScope, FunctionBody.exprBoundNames,\n stmtNextScope, permitScope, permitStructHashStmt,\n collectStmtNames,\n Compiler.Modules.Hashing.eip712HashStruct,\n Compiler.Modules.Hashing.abiEncodeStaticWords,\n Compiler.Modules.Hashing.abiEncodeStaticWordsModule]\n\n","fan_in":1,"n_lines":29,"n_chars":1279,"n_subproofs":0,"n_tactics":30,"cyclomatic":11,"n_automation":24,"n_rewrites":1,"n_structural":13,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"permitStaticHashAndDigest_supported\",\n \"text\": \"private theorem permitStaticHashAndDigest_supported :\\n SupportedStmtList [] permitScope permitStaticHashAndDigestStmts := by\\n change SupportedStmtList [] permitScope ([permitStructHashStmt] ++ [permitDigestStmt])\\n apply SupportedStmtList.append\\n · apply SupportedStmtList.pureHashingEcm\\n · simp [ecmPureHashing, Compiler.Modules.Hashing.abiEncodeStaticWordsModule]\\n · intro a ha\\n simp at ha\\n rcases ha with rfl | rfl | rfl | rfl | rfl | rfl <;> constructor\\n · intro a ha\\n simp at ha\\n rcases ha with rfl | rfl | rfl | rfl | rfl | rfl <;>\\n simp [FunctionBody.exprBoundNamesInScope, FunctionBody.exprBoundNames, permitScope]\\n · apply SupportedStmtList.pureHashingEcm\\n · simp [ecmPureHashing, Compiler.Modules.Hashing.eip712DigestModule]\\n · intro a ha\\n simp at ha\\n rcases ha with rfl | rfl <;> constructor\\n · intro a ha\\n simp at ha\\n rcases ha with rfl | rfl <;>\\n simp [FunctionBody.exprBoundNamesInScope, FunctionBody.exprBoundNames,\\n stmtNextScope, permitScope, permitStructHashStmt,\\n collectStmtNames,\\n Compiler.Modules.Hashing.eip712HashStruct,\\n Compiler.Modules.Hashing.abiEncodeStaticWords,\\n Compiler.Modules.Hashing.abiEncodeStaticWordsModule]\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 29,\n \"n_chars\": 1279,\n \"n_subproofs\": 0,\n \"n_tactics\": 30,\n \"cyclomatic\": 11,\n \"n_automation\": 24,\n \"n_rewrites\": 1,\n \"n_structural\": 13,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"permitStaticHash_eip712Supported_and_digest_correct","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":16,"n_chars":572,"n_subproofs":0,"n_tactics":11,"cyclomatic":5,"n_automation":2,"n_rewrites":0,"n_structural":7,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"permitStaticHash_eip712Supported_and_digest_correct\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 16,\n \"n_chars\": 572,\n \"n_subproofs\": 0,\n \"n_tactics\": 11,\n \"cyclomatic\": 5,\n \"n_automation\": 2,\n \"n_rewrites\": 0,\n \"n_structural\": 7,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Contracts.Common\nimport Compiler.Modules.Hashing\nimport Compiler.Proofs.IRGeneration.SupportedSpec\n\nnamespace Contracts.Smoke\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Proofs.IRGeneration\nopen Compiler.Yul\nopen Verity hiding pure bind\n\ndef permitTypeHash : Nat :=\n (keccakString \"Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)\").val\n\ndef permitStaticHashArgs : List Expr :=\n [ Expr.literal permitTypeHash\n , Expr.param \"owner\"\n , Expr.param \"spender\"\n , Expr.param \"value\"\n , Expr.param \"nonce\"\n , Expr.param \"deadline\"\n ]\n\ndef permitStructHashStmt : Stmt :=\n Compiler.Modules.Hashing.eip712HashStruct\n \"structHash\" (Expr.literal permitTypeHash)\n [ Expr.param \"owner\"\n , Expr.param \"spender\"\n , Expr.param \"value\"\n , Expr.param \"nonce\"\n , Expr.param \"deadline\"\n ]\n\ndef permitDigestStmt : Stmt :=\n Compiler.Modules.Hashing.eip712Digest\n \"digest\" (Expr.param \"domainSeparator\") (Expr.localVar \"structHash\")\n\ndef permitStaticHashAndDigestStmts : List Stmt :=\n [permitStructHashStmt, permitDigestStmt]\n\ndef permitScope : List String :=\n [\"domainSeparator\", \"owner\", \"spender\", \"value\", \"nonce\", \"deadline\"]\n\ndef permitStaticStructHashLayoutCorrect : Prop :=\n (Compiler.Modules.Hashing.abiEncodeStaticWordsModule \"structHash\" 6).axioms =\n [\"keccak256_memory_slice_matches_evm\", \"abi_standard_static_word_layout\"] ∧\n (Compiler.Modules.Hashing.abiEncodeStaticWordsModule \"structHash\" 6).compile {}\n [ YulExpr.lit permitTypeHash\n , YulExpr.ident \"owner\"\n , YulExpr.ident \"spender\"\n , YulExpr.ident \"value\"\n , YulExpr.ident \"nonce\"\n , YulExpr.ident \"deadline\"\n ] =\n Except.ok (Compiler.Modules.Hashing.permitStructHashExpectedYul permitTypeHash)\n\ndef permitStaticDigestLayoutCorrect : Prop :=\n (Compiler.Modules.Hashing.eip712DigestModule \"digest\").axioms =\n [\"keccak256_memory_slice_matches_evm\", \"eip712_digest_layout\"] ∧\n (Compiler.Modules.Hashing.eip712DigestModule \"digest\").compile {}\n [YulExpr.ident \"domainSeparator\", YulExpr.ident \"structHash\"] =\n Except.ok Compiler.Modules.Hashing.eip712DigestExpectedYul\n\ntheorem permitStaticHash_eip712Supported_and_digest_correct :\n SupportedStmtList [] permitScope permitStaticHashAndDigestStmts ∧\n permitStaticStructHashLayoutCorrect ∧\n permitStaticDigestLayoutCorrect := by\n constructor\n · sorry\n · constructor\n · constructor\n · rfl\n · exact Compiler.Modules.Hashing.abiEncodeStaticWordsModule_compile_permitStructHash_layout\n permitTypeHash\n · constructor\n · rfl\n · exact Compiler.Modules.Hashing.eip712DigestModule_compile_digest_layout\n\nset_option linter.unusedVariables false in\nverity_contract EIP712StaticSmoke where\n storage\n\n function recoverPermitSigner\n (domainSeparator : Bytes32, owner : Address, spender : Address,\n value : Uint256, nonce : Uint256, deadline : Uint256,\n v : Uint256, r : Bytes32, s : Bytes32) : Address := do\n let structHash ← ecmCall\n (fun resultVar => Compiler.Modules.Hashing.abiEncodeStaticWordsModule resultVar 6)\n [keccakString \"Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)\",\n addressToWord owner, addressToWord spender, value, nonce, deadline]\n let digest ← ecmCall Compiler.Modules.Hashing.eip712DigestModule\n [domainSeparator, structHash]\n let signer ← ecrecover digest v r s\n return signer\n\nexample :\n EIP712StaticSmoke.recoverPermitSigner_modelBody =\n [ permitStructHashStmt\n , permitDigestStmt\n , Compiler.Modules.Precompiles.ecrecover\n \"signer\" (Expr.localVar \"digest\") (Expr.param \"v\") (Expr.param \"r\") (Expr.param \"s\")\n , Stmt.return (Expr.localVar \"signer\")\n ] := rfl\n\nend Contracts.Smoke\n"},"solution_file_content":{"kind":"string","value":"import Contracts.Common\nimport Compiler.Modules.Hashing\nimport Compiler.Proofs.IRGeneration.SupportedSpec\n\nnamespace Contracts.Smoke\n\nopen Compiler\nopen Compiler.CompilationModel\nopen Compiler.Proofs.IRGeneration\nopen Compiler.Yul\nopen Verity hiding pure bind\n\ndef permitTypeHash : Nat :=\n (keccakString \"Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)\").val\n\ndef permitStaticHashArgs : List Expr :=\n [ Expr.literal permitTypeHash\n , Expr.param \"owner\"\n , Expr.param \"spender\"\n , Expr.param \"value\"\n , Expr.param \"nonce\"\n , Expr.param \"deadline\"\n ]\n\ndef permitStructHashStmt : Stmt :=\n Compiler.Modules.Hashing.eip712HashStruct\n \"structHash\" (Expr.literal permitTypeHash)\n [ Expr.param \"owner\"\n , Expr.param \"spender\"\n , Expr.param \"value\"\n , Expr.param \"nonce\"\n , Expr.param \"deadline\"\n ]\n\ndef permitDigestStmt : Stmt :=\n Compiler.Modules.Hashing.eip712Digest\n \"digest\" (Expr.param \"domainSeparator\") (Expr.localVar \"structHash\")\n\ndef permitStaticHashAndDigestStmts : List Stmt :=\n [permitStructHashStmt, permitDigestStmt]\n\ndef permitScope : List String :=\n [\"domainSeparator\", \"owner\", \"spender\", \"value\", \"nonce\", \"deadline\"]\n\ndef permitStaticStructHashLayoutCorrect : Prop :=\n (Compiler.Modules.Hashing.abiEncodeStaticWordsModule \"structHash\" 6).axioms =\n [\"keccak256_memory_slice_matches_evm\", \"abi_standard_static_word_layout\"] ∧\n (Compiler.Modules.Hashing.abiEncodeStaticWordsModule \"structHash\" 6).compile {}\n [ YulExpr.lit permitTypeHash\n , YulExpr.ident \"owner\"\n , YulExpr.ident \"spender\"\n , YulExpr.ident \"value\"\n , YulExpr.ident \"nonce\"\n , YulExpr.ident \"deadline\"\n ] =\n Except.ok (Compiler.Modules.Hashing.permitStructHashExpectedYul permitTypeHash)\n\ndef permitStaticDigestLayoutCorrect : Prop :=\n (Compiler.Modules.Hashing.eip712DigestModule \"digest\").axioms =\n [\"keccak256_memory_slice_matches_evm\", \"eip712_digest_layout\"] ∧\n (Compiler.Modules.Hashing.eip712DigestModule \"digest\").compile {}\n [YulExpr.ident \"domainSeparator\", YulExpr.ident \"structHash\"] =\n Except.ok Compiler.Modules.Hashing.eip712DigestExpectedYul\n\nprivate theorem permitStaticHashAndDigest_supported :\n SupportedStmtList [] permitScope permitStaticHashAndDigestStmts := by\n change SupportedStmtList [] permitScope ([permitStructHashStmt] ++ [permitDigestStmt])\n apply SupportedStmtList.append\n · apply SupportedStmtList.pureHashingEcm\n · simp [ecmPureHashing, Compiler.Modules.Hashing.abiEncodeStaticWordsModule]\n · intro a ha\n simp at ha\n rcases ha with rfl | rfl | rfl | rfl | rfl | rfl <;> constructor\n · intro a ha\n simp at ha\n rcases ha with rfl | rfl | rfl | rfl | rfl | rfl <;>\n simp [FunctionBody.exprBoundNamesInScope, FunctionBody.exprBoundNames, permitScope]\n · apply SupportedStmtList.pureHashingEcm\n · simp [ecmPureHashing, Compiler.Modules.Hashing.eip712DigestModule]\n · intro a ha\n simp at ha\n rcases ha with rfl | rfl <;> constructor\n · intro a ha\n simp at ha\n rcases ha with rfl | rfl <;>\n simp [FunctionBody.exprBoundNamesInScope, FunctionBody.exprBoundNames,\n stmtNextScope, permitScope, permitStructHashStmt,\n collectStmtNames,\n Compiler.Modules.Hashing.eip712HashStruct,\n Compiler.Modules.Hashing.abiEncodeStaticWords,\n Compiler.Modules.Hashing.abiEncodeStaticWordsModule]\n\ntheorem permitStaticHash_eip712Supported_and_digest_correct :\n SupportedStmtList [] permitScope permitStaticHashAndDigestStmts ∧\n permitStaticStructHashLayoutCorrect ∧\n permitStaticDigestLayoutCorrect := by\n constructor\n · exact permitStaticHashAndDigest_supported\n · constructor\n · constructor\n · rfl\n · exact Compiler.Modules.Hashing.abiEncodeStaticWordsModule_compile_permitStructHash_layout\n permitTypeHash\n · constructor\n · rfl\n · exact Compiler.Modules.Hashing.eip712DigestModule_compile_digest_layout\n\nset_option linter.unusedVariables false in\nverity_contract EIP712StaticSmoke where\n storage\n\n function recoverPermitSigner\n (domainSeparator : Bytes32, owner : Address, spender : Address,\n value : Uint256, nonce : Uint256, deadline : Uint256,\n v : Uint256, r : Bytes32, s : Bytes32) : Address := do\n let structHash ← ecmCall\n (fun resultVar => Compiler.Modules.Hashing.abiEncodeStaticWordsModule resultVar 6)\n [keccakString \"Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)\",\n addressToWord owner, addressToWord spender, value, nonce, deadline]\n let digest ← ecmCall Compiler.Modules.Hashing.eip712DigestModule\n [domainSeparator, structHash]\n let signer ← ecrecover digest v r s\n return signer\n\nexample :\n EIP712StaticSmoke.recoverPermitSigner_modelBody =\n [ permitStructHashStmt\n , permitDigestStmt\n , Compiler.Modules.Precompiles.ecrecover\n \"signer\" (Expr.localVar \"digest\") (Expr.param \"v\") (Expr.param \"r\") (Expr.param \"s\")\n , Stmt.return (Expr.localVar \"signer\")\n ] := rfl\n\nend Contracts.Smoke\n"},"solution_diff":{"kind":"string","value":"@@ -62,12 +62,40 @@\n [YulExpr.ident \"domainSeparator\", YulExpr.ident \"structHash\"] =\n Except.ok Compiler.Modules.Hashing.eip712DigestExpectedYul\n \n+private theorem permitStaticHashAndDigest_supported :\n+ SupportedStmtList [] permitScope permitStaticHashAndDigestStmts := by\n+ change SupportedStmtList [] permitScope ([permitStructHashStmt] ++ [permitDigestStmt])\n+ apply SupportedStmtList.append\n+ · apply SupportedStmtList.pureHashingEcm\n+ · simp [ecmPureHashing, Compiler.Modules.Hashing.abiEncodeStaticWordsModule]\n+ · intro a ha\n+ simp at ha\n+ rcases ha with rfl | rfl | rfl | rfl | rfl | rfl <;> constructor\n+ · intro a ha\n+ simp at ha\n+ rcases ha with rfl | rfl | rfl | rfl | rfl | rfl <;>\n+ simp [FunctionBody.exprBoundNamesInScope, FunctionBody.exprBoundNames, permitScope]\n+ · apply SupportedStmtList.pureHashingEcm\n+ · simp [ecmPureHashing, Compiler.Modules.Hashing.eip712DigestModule]\n+ · intro a ha\n+ simp at ha\n+ rcases ha with rfl | rfl <;> constructor\n+ · intro a ha\n+ simp at ha\n+ rcases ha with rfl | rfl <;>\n+ simp [FunctionBody.exprBoundNamesInScope, FunctionBody.exprBoundNames,\n+ stmtNextScope, permitScope, permitStructHashStmt,\n+ collectStmtNames,\n+ Compiler.Modules.Hashing.eip712HashStruct,\n+ Compiler.Modules.Hashing.abiEncodeStaticWords,\n+ Compiler.Modules.Hashing.abiEncodeStaticWordsModule]\n+\n theorem permitStaticHash_eip712Supported_and_digest_correct :\n SupportedStmtList [] permitScope permitStaticHashAndDigestStmts ∧\n permitStaticStructHashLayoutCorrect ∧\n permitStaticDigestLayoutCorrect := by\n constructor\n- · sorry\n+ · exact permitStaticHashAndDigest_supported\n · constructor\n · constructor\n · rfl\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21384,"cells":{"task_id":{"kind":"string","value":"ablate_bd1f7089f857_0"},"challenge_id":{"kind":"string","value":"fe19b59a09e8928b"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/EVM/Frame.lean"},"theory":{"kind":"string","value":"Frame"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"external_call_preserves_caller_memory","depth":1,"n_commands":0,"n_lines":4,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n apply external_call_preserves_caller_memory_outside_output_buffer\n rintro ⟨h1, h2⟩\n rcases hDisj with h | h <;> omega","n_chars":129,"n_subproofs":0,"n_tactics":5,"cyclomatic":4,"n_automation":1,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"theorem_name\": \"external_call_preserves_caller_memory\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 4,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n apply external_call_preserves_caller_memory_outside_output_buffer\\n rintro ⟨h1, h2⟩\\n rcases hDisj with h | h <;> omega\",\n \"n_chars\": 129,\n \"n_subproofs\": 0,\n \"n_tactics\": 5,\n \"cyclomatic\": 4,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"external_call_preserves_caller_memory_outside_output_buffer","text":"theorem external_call_preserves_caller_memory_outside_output_buffer\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (i : Nat) (hOutside : ¬ (outOff ≤ i ∧ i < outOff + outSize)) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n caller.memory i := by\n simp [applyCallToCaller, hOutside]\n\n","fan_in":1,"n_lines":8,"n_chars":344,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":true,"max_nesting":2}],"string":"[\n {\n \"name\": \"external_call_preserves_caller_memory_outside_output_buffer\",\n \"text\": \"theorem external_call_preserves_caller_memory_outside_output_buffer\\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\\n (i : Nat) (hOutside : ¬ (outOff ≤ i ∧ i < outOff + outSize)) :\\n (applyCallToCaller caller outOff outSize callee).memory i =\\n caller.memory i := by\\n simp [applyCallToCaller, hOutside]\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 8,\n \"n_chars\": 344,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": true,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"external_call_preserves_caller_memory","fan_in":1,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":16,"n_chars":669,"n_subproofs":0,"n_tactics":5,"cyclomatic":4,"n_automation":1,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"external_call_preserves_caller_memory\",\n \"fan_in\": 1,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 16,\n \"n_chars\": 669,\n \"n_subproofs\": 0,\n \"n_tactics\": 5,\n \"cyclomatic\": 4,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Verity.EVM.Uint256\nimport Verity.EVM.MemoryModel\nimport Verity.Core.Uint256\n\nnamespace Verity.EVM.Frame\n\nopen Verity.Core (Uint256)\nopen Verity.EVM.MemoryModel\n\n/-!\n# EVM `CALL` boundary frame conditions\n\nModels the slice of EVM `CALL` semantics that touches the caller's\nframe, and proves the frame conditions that downstream contract proofs\nneed to reason about external calls without quantifying over callee\nbytecode.\n\nPromoted from `Benchmark.Cases.ERC4337.EntryPointInvariant.EvmYulFrame`.\n\n## What this discharges\n\nBefore this module, every benchmark that touched external calls had to\nassume (or reproduce in their own file) the EVM-level frame condition\nthat external `CALL` cannot SSTORE the caller's slots and cannot write\nto caller memory outside the declared output buffer. That assumption is\ndocumented in `AXIOMS.md` under \"External Call Module\". This module\nmakes the assumption a *theorem* of `Verity.EVM`, parameterised over an\nabstract `CalleeResult` whose universal quantification over its\ninhabitants is equivalent to quantifying over arbitrary EVM callee\nbytecode.\n\n## Roadmap\n\nA subsequent PR will prove that this abstract `CallerFrame` /\n`CalleeResult` model is the projection of EvmYul's actual `CALL` opcode\nsemantics, closing the gap between this layer and the deeper EvmYul\ncorrectness theorems.\n-/\n\n/-- An EVM address (160-bit; we expose identity only). -/\nabbrev Address := Nat\n\n/-- The caller-side EVM frame at a `CALL` boundary. The four mutable\n sub-states the EVM exposes to a contract are modelled explicitly. -/\nstructure CallerFrame where\n thisAddress : Address\n memory : Nat → Uint256\n storageMap : Nat → Uint256\n transientStorage : Nat → Uint256\n returnDataBuf : Nat → Uint256\n\n/-- Everything an arbitrary callee can return to the caller across a\n `CALL` boundary. The callee's internal storage updates are scoped to\n its own address and so do not appear here — they cannot affect the\n caller's frame. Quantifying over inhabitants of this type is\n equivalent to quantifying over arbitrary EVM callee programs that\n produce any `(success, returndata)` pair. -/\nstructure CalleeResult where\n success : Uint256\n returnedData : Nat → Uint256\n\n/-- The portion of EVM `CALL` semantics that touches the caller's frame.\n\nBy the Yellow Paper, `CALL` to a target ≠ self with the caller's output\nbuffer `[outOff, outOff + outSize)` updates the caller's memory by\ncopying `outSize` words of the callee's returndata into that range,\nleaves storage and transient storage untouched, and writes the new\nreturndata buffer to the caller's `returnDataBuf`. -/\ndef applyCallToCaller\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n : CallerFrame :=\n { caller with\n memory := fun i =>\n if outOff ≤ i ∧ i < outOff + outSize then\n callee.returnedData (i - outOff)\n else\n caller.memory i\n returnDataBuf := callee.returnedData }\n\n/-! ## Single-CALL frame theorems -/\n\n/-- Headline form: caller-memory preservation under a disjoint output\n buffer. Composes directly with `MemoryModel.Disjoint`. -/\ntheorem external_call_preserves_caller_memory\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (regionLo regionHi : Nat)\n (hDisj : outOff + outSize ≤ regionLo ∨ regionHi ≤ outOff)\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n caller.memory i := sorry\n\n/-! ## Iterated-CALL frame theorems -/\n\nend Verity.EVM.Frame\n"},"solution_file_content":{"kind":"string","value":"import Verity.EVM.Uint256\nimport Verity.EVM.MemoryModel\nimport Verity.Core.Uint256\n\nnamespace Verity.EVM.Frame\n\nopen Verity.Core (Uint256)\nopen Verity.EVM.MemoryModel\n\n/-!\n# EVM `CALL` boundary frame conditions\n\nModels the slice of EVM `CALL` semantics that touches the caller's\nframe, and proves the frame conditions that downstream contract proofs\nneed to reason about external calls without quantifying over callee\nbytecode.\n\nPromoted from `Benchmark.Cases.ERC4337.EntryPointInvariant.EvmYulFrame`.\n\n## What this discharges\n\nBefore this module, every benchmark that touched external calls had to\nassume (or reproduce in their own file) the EVM-level frame condition\nthat external `CALL` cannot SSTORE the caller's slots and cannot write\nto caller memory outside the declared output buffer. That assumption is\ndocumented in `AXIOMS.md` under \"External Call Module\". This module\nmakes the assumption a *theorem* of `Verity.EVM`, parameterised over an\nabstract `CalleeResult` whose universal quantification over its\ninhabitants is equivalent to quantifying over arbitrary EVM callee\nbytecode.\n\n## Roadmap\n\nA subsequent PR will prove that this abstract `CallerFrame` /\n`CalleeResult` model is the projection of EvmYul's actual `CALL` opcode\nsemantics, closing the gap between this layer and the deeper EvmYul\ncorrectness theorems.\n-/\n\n/-- An EVM address (160-bit; we expose identity only). -/\nabbrev Address := Nat\n\n/-- The caller-side EVM frame at a `CALL` boundary. The four mutable\n sub-states the EVM exposes to a contract are modelled explicitly. -/\nstructure CallerFrame where\n thisAddress : Address\n memory : Nat → Uint256\n storageMap : Nat → Uint256\n transientStorage : Nat → Uint256\n returnDataBuf : Nat → Uint256\n\n/-- Everything an arbitrary callee can return to the caller across a\n `CALL` boundary. The callee's internal storage updates are scoped to\n its own address and so do not appear here — they cannot affect the\n caller's frame. Quantifying over inhabitants of this type is\n equivalent to quantifying over arbitrary EVM callee programs that\n produce any `(success, returndata)` pair. -/\nstructure CalleeResult where\n success : Uint256\n returnedData : Nat → Uint256\n\n/-- The portion of EVM `CALL` semantics that touches the caller's frame.\n\nBy the Yellow Paper, `CALL` to a target ≠ self with the caller's output\nbuffer `[outOff, outOff + outSize)` updates the caller's memory by\ncopying `outSize` words of the callee's returndata into that range,\nleaves storage and transient storage untouched, and writes the new\nreturndata buffer to the caller's `returnDataBuf`. -/\ndef applyCallToCaller\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n : CallerFrame :=\n { caller with\n memory := fun i =>\n if outOff ≤ i ∧ i < outOff + outSize then\n callee.returnedData (i - outOff)\n else\n caller.memory i\n returnDataBuf := callee.returnedData }\n\n/-! ## Single-CALL frame theorems -/\n\ntheorem external_call_preserves_caller_memory_outside_output_buffer\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (i : Nat) (hOutside : ¬ (outOff ≤ i ∧ i < outOff + outSize)) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n caller.memory i := by\n simp [applyCallToCaller, hOutside]\n\n/-- Headline form: caller-memory preservation under a disjoint output\n buffer. Composes directly with `MemoryModel.Disjoint`. -/\ntheorem external_call_preserves_caller_memory\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (regionLo regionHi : Nat)\n (hDisj : outOff + outSize ≤ regionLo ∨ regionHi ≤ outOff)\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n caller.memory i := by\n apply external_call_preserves_caller_memory_outside_output_buffer\n rintro ⟨h1, h2⟩\n rcases hDisj with h | h <;> omega\n\n/-! ## Iterated-CALL frame theorems -/\n\nend Verity.EVM.Frame\n"},"solution_diff":{"kind":"string","value":"@@ -79,6 +79,13 @@\n \n /-! ## Single-CALL frame theorems -/\n \n+theorem external_call_preserves_caller_memory_outside_output_buffer\n+ (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n+ (i : Nat) (hOutside : ¬ (outOff ≤ i ∧ i < outOff + outSize)) :\n+ (applyCallToCaller caller outOff outSize callee).memory i =\n+ caller.memory i := by\n+ simp [applyCallToCaller, hOutside]\n+\n /-- Headline form: caller-memory preservation under a disjoint output\n buffer. Composes directly with `MemoryModel.Disjoint`. -/\n theorem external_call_preserves_caller_memory\n@@ -87,7 +94,10 @@\n (hDisj : outOff + outSize ≤ regionLo ∨ regionHi ≤ outOff)\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n- caller.memory i := sorry\n+ caller.memory i := by\n+ apply external_call_preserves_caller_memory_outside_output_buffer\n+ rintro ⟨h1, h2⟩\n+ rcases hDisj with h | h <;> omega\n \n /-! ## Iterated-CALL frame theorems -/\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21385,"cells":{"task_id":{"kind":"string","value":"ablate_bd1f7089f857_1"},"challenge_id":{"kind":"string","value":"2374913f63f8213c"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/EVM/Frame.lean"},"theory":{"kind":"string","value":"Frame"},"variant":{"kind":"number","value":1,"string":"1"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"external_calls_preserve_caller_storage","depth":1,"n_commands":0,"n_lines":7,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n have hStep := external_call_preserves_caller_storage caller c.1 c.2.1 c.2.2 slotIdx\n have := ih (applyCallToCaller caller c.1 c.2.1 c.2.2)\n simp [List.foldl]; rw [this, hStep]","n_chars":269,"n_subproofs":2,"n_tactics":8,"cyclomatic":2,"n_automation":2,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"theorem_name\": \"external_calls_preserve_caller_storage\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 7,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction calls generalizing caller with\\n | nil => rfl\\n | cons c rest ih =>\\n have hStep := external_call_preserves_caller_storage caller c.1 c.2.1 c.2.2 slotIdx\\n have := ih (applyCallToCaller caller c.1 c.2.1 c.2.2)\\n simp [List.foldl]; rw [this, hStep]\",\n \"n_chars\": 269,\n \"n_subproofs\": 2,\n \"n_tactics\": 8,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"external_call_preserves_caller_storage","text":"theorem external_call_preserves_caller_storage\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (slotIdx : Nat) :\n (applyCallToCaller caller outOff outSize callee).storageMap slotIdx =\n caller.storageMap slotIdx := by\n simp [applyCallToCaller]\n\n","fan_in":1,"n_lines":8,"n_chars":283,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":true,"max_nesting":2}],"string":"[\n {\n \"name\": \"external_call_preserves_caller_storage\",\n \"text\": \"theorem external_call_preserves_caller_storage\\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\\n (slotIdx : Nat) :\\n (applyCallToCaller caller outOff outSize callee).storageMap slotIdx =\\n caller.storageMap slotIdx := by\\n simp [applyCallToCaller]\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 8,\n \"n_chars\": 283,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": true,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"external_calls_preserve_caller_storage","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":15,"n_chars":548,"n_subproofs":2,"n_tactics":8,"cyclomatic":2,"n_automation":2,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":4}],"string":"[\n {\n \"name\": \"external_calls_preserve_caller_storage\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 15,\n \"n_chars\": 548,\n \"n_subproofs\": 2,\n \"n_tactics\": 8,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 4\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Verity.EVM.Uint256\nimport Verity.EVM.MemoryModel\nimport Verity.Core.Uint256\n\nnamespace Verity.EVM.Frame\n\nopen Verity.Core (Uint256)\nopen Verity.EVM.MemoryModel\n\n/-!\n# EVM `CALL` boundary frame conditions\n\nModels the slice of EVM `CALL` semantics that touches the caller's\nframe, and proves the frame conditions that downstream contract proofs\nneed to reason about external calls without quantifying over callee\nbytecode.\n\nPromoted from `Benchmark.Cases.ERC4337.EntryPointInvariant.EvmYulFrame`.\n\n## What this discharges\n\nBefore this module, every benchmark that touched external calls had to\nassume (or reproduce in their own file) the EVM-level frame condition\nthat external `CALL` cannot SSTORE the caller's slots and cannot write\nto caller memory outside the declared output buffer. That assumption is\ndocumented in `AXIOMS.md` under \"External Call Module\". This module\nmakes the assumption a *theorem* of `Verity.EVM`, parameterised over an\nabstract `CalleeResult` whose universal quantification over its\ninhabitants is equivalent to quantifying over arbitrary EVM callee\nbytecode.\n\n## Roadmap\n\nA subsequent PR will prove that this abstract `CallerFrame` /\n`CalleeResult` model is the projection of EvmYul's actual `CALL` opcode\nsemantics, closing the gap between this layer and the deeper EvmYul\ncorrectness theorems.\n-/\n\n/-- An EVM address (160-bit; we expose identity only). -/\nabbrev Address := Nat\n\n/-- The caller-side EVM frame at a `CALL` boundary. The four mutable\n sub-states the EVM exposes to a contract are modelled explicitly. -/\nstructure CallerFrame where\n thisAddress : Address\n memory : Nat → Uint256\n storageMap : Nat → Uint256\n transientStorage : Nat → Uint256\n returnDataBuf : Nat → Uint256\n\n/-- Everything an arbitrary callee can return to the caller across a\n `CALL` boundary. The callee's internal storage updates are scoped to\n its own address and so do not appear here — they cannot affect the\n caller's frame. Quantifying over inhabitants of this type is\n equivalent to quantifying over arbitrary EVM callee programs that\n produce any `(success, returndata)` pair. -/\nstructure CalleeResult where\n success : Uint256\n returnedData : Nat → Uint256\n\n/-- The portion of EVM `CALL` semantics that touches the caller's frame.\n\nBy the Yellow Paper, `CALL` to a target ≠ self with the caller's output\nbuffer `[outOff, outOff + outSize)` updates the caller's memory by\ncopying `outSize` words of the callee's returndata into that range,\nleaves storage and transient storage untouched, and writes the new\nreturndata buffer to the caller's `returnDataBuf`. -/\ndef applyCallToCaller\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n : CallerFrame :=\n { caller with\n memory := fun i =>\n if outOff ≤ i ∧ i < outOff + outSize then\n callee.returnedData (i - outOff)\n else\n caller.memory i\n returnDataBuf := callee.returnedData }\n\n/-! ## Single-CALL frame theorems -/\n\ntheorem external_calls_preserve_caller_storage\n (caller : CallerFrame)\n (calls : List (Nat × Nat × CalleeResult))\n (slotIdx : Nat) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).storageMap slotIdx =\n caller.storageMap slotIdx := sorry\n\nend Verity.EVM.Frame\n"},"solution_file_content":{"kind":"string","value":"import Verity.EVM.Uint256\nimport Verity.EVM.MemoryModel\nimport Verity.Core.Uint256\n\nnamespace Verity.EVM.Frame\n\nopen Verity.Core (Uint256)\nopen Verity.EVM.MemoryModel\n\n/-!\n# EVM `CALL` boundary frame conditions\n\nModels the slice of EVM `CALL` semantics that touches the caller's\nframe, and proves the frame conditions that downstream contract proofs\nneed to reason about external calls without quantifying over callee\nbytecode.\n\nPromoted from `Benchmark.Cases.ERC4337.EntryPointInvariant.EvmYulFrame`.\n\n## What this discharges\n\nBefore this module, every benchmark that touched external calls had to\nassume (or reproduce in their own file) the EVM-level frame condition\nthat external `CALL` cannot SSTORE the caller's slots and cannot write\nto caller memory outside the declared output buffer. That assumption is\ndocumented in `AXIOMS.md` under \"External Call Module\". This module\nmakes the assumption a *theorem* of `Verity.EVM`, parameterised over an\nabstract `CalleeResult` whose universal quantification over its\ninhabitants is equivalent to quantifying over arbitrary EVM callee\nbytecode.\n\n## Roadmap\n\nA subsequent PR will prove that this abstract `CallerFrame` /\n`CalleeResult` model is the projection of EvmYul's actual `CALL` opcode\nsemantics, closing the gap between this layer and the deeper EvmYul\ncorrectness theorems.\n-/\n\n/-- An EVM address (160-bit; we expose identity only). -/\nabbrev Address := Nat\n\n/-- The caller-side EVM frame at a `CALL` boundary. The four mutable\n sub-states the EVM exposes to a contract are modelled explicitly. -/\nstructure CallerFrame where\n thisAddress : Address\n memory : Nat → Uint256\n storageMap : Nat → Uint256\n transientStorage : Nat → Uint256\n returnDataBuf : Nat → Uint256\n\n/-- Everything an arbitrary callee can return to the caller across a\n `CALL` boundary. The callee's internal storage updates are scoped to\n its own address and so do not appear here — they cannot affect the\n caller's frame. Quantifying over inhabitants of this type is\n equivalent to quantifying over arbitrary EVM callee programs that\n produce any `(success, returndata)` pair. -/\nstructure CalleeResult where\n success : Uint256\n returnedData : Nat → Uint256\n\n/-- The portion of EVM `CALL` semantics that touches the caller's frame.\n\nBy the Yellow Paper, `CALL` to a target ≠ self with the caller's output\nbuffer `[outOff, outOff + outSize)` updates the caller's memory by\ncopying `outSize` words of the callee's returndata into that range,\nleaves storage and transient storage untouched, and writes the new\nreturndata buffer to the caller's `returnDataBuf`. -/\ndef applyCallToCaller\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n : CallerFrame :=\n { caller with\n memory := fun i =>\n if outOff ≤ i ∧ i < outOff + outSize then\n callee.returnedData (i - outOff)\n else\n caller.memory i\n returnDataBuf := callee.returnedData }\n\n/-! ## Single-CALL frame theorems -/\n\ntheorem external_call_preserves_caller_storage\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (slotIdx : Nat) :\n (applyCallToCaller caller outOff outSize callee).storageMap slotIdx =\n caller.storageMap slotIdx := by\n simp [applyCallToCaller]\n\ntheorem external_calls_preserve_caller_storage\n (caller : CallerFrame)\n (calls : List (Nat × Nat × CalleeResult))\n (slotIdx : Nat) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).storageMap slotIdx =\n caller.storageMap slotIdx := by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n have hStep := external_call_preserves_caller_storage caller c.1 c.2.1 c.2.2 slotIdx\n have := ih (applyCallToCaller caller c.1 c.2.1 c.2.2)\n simp [List.foldl]; rw [this, hStep]\n\nend Verity.EVM.Frame\n"},"solution_diff":{"kind":"string","value":"@@ -79,13 +79,26 @@\n \n /-! ## Single-CALL frame theorems -/\n \n+theorem external_call_preserves_caller_storage\n+ (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n+ (slotIdx : Nat) :\n+ (applyCallToCaller caller outOff outSize callee).storageMap slotIdx =\n+ caller.storageMap slotIdx := by\n+ simp [applyCallToCaller]\n+\n theorem external_calls_preserve_caller_storage\n (caller : CallerFrame)\n (calls : List (Nat × Nat × CalleeResult))\n (slotIdx : Nat) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).storageMap slotIdx =\n- caller.storageMap slotIdx := sorry\n+ caller.storageMap slotIdx := by\n+ induction calls generalizing caller with\n+ | nil => rfl\n+ | cons c rest ih =>\n+ have hStep := external_call_preserves_caller_storage caller c.1 c.2.1 c.2.2 slotIdx\n+ have := ih (applyCallToCaller caller c.1 c.2.1 c.2.2)\n+ simp [List.foldl]; rw [this, hStep]\n \n end Verity.EVM.Frame\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21386,"cells":{"task_id":{"kind":"string","value":"ablate_bd1f7089f857_2"},"challenge_id":{"kind":"string","value":"c8321e8396fe53a4"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/EVM/Frame.lean"},"theory":{"kind":"string","value":"Frame"},"variant":{"kind":"number","value":2,"string":"2"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"external_calls_preserve_caller_transient_storage","depth":1,"n_commands":0,"n_lines":8,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n have hStep := external_call_preserves_caller_transient_storage\n caller c.1 c.2.1 c.2.2 slotIdx\n have := ih (applyCallToCaller caller c.1 c.2.1 c.2.2)\n simp [List.foldl]; rw [this, hStep]","n_chars":285,"n_subproofs":2,"n_tactics":9,"cyclomatic":2,"n_automation":2,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"theorem_name\": \"external_calls_preserve_caller_transient_storage\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 8,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction calls generalizing caller with\\n | nil => rfl\\n | cons c rest ih =>\\n have hStep := external_call_preserves_caller_transient_storage\\n caller c.1 c.2.1 c.2.2 slotIdx\\n have := ih (applyCallToCaller caller c.1 c.2.1 c.2.2)\\n simp [List.foldl]; rw [this, hStep]\",\n \"n_chars\": 285,\n \"n_subproofs\": 2,\n \"n_tactics\": 9,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"external_call_preserves_caller_transient_storage","text":"theorem external_call_preserves_caller_transient_storage\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (slotIdx : Nat) :\n (applyCallToCaller caller outOff outSize callee).transientStorage slotIdx =\n caller.transientStorage slotIdx := by\n simp [applyCallToCaller]\n\n","fan_in":1,"n_lines":8,"n_chars":305,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":true,"max_nesting":2}],"string":"[\n {\n \"name\": \"external_call_preserves_caller_transient_storage\",\n \"text\": \"theorem external_call_preserves_caller_transient_storage\\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\\n (slotIdx : Nat) :\\n (applyCallToCaller caller outOff outSize callee).transientStorage slotIdx =\\n caller.transientStorage slotIdx := by\\n simp [applyCallToCaller]\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 8,\n \"n_chars\": 305,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": true,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"external_calls_preserve_caller_transient_storage","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":16,"n_chars":586,"n_subproofs":2,"n_tactics":9,"cyclomatic":2,"n_automation":2,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"external_calls_preserve_caller_transient_storage\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 16,\n \"n_chars\": 586,\n \"n_subproofs\": 2,\n \"n_tactics\": 9,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Verity.EVM.Uint256\nimport Verity.EVM.MemoryModel\nimport Verity.Core.Uint256\n\nnamespace Verity.EVM.Frame\n\nopen Verity.Core (Uint256)\nopen Verity.EVM.MemoryModel\n\n/-!\n# EVM `CALL` boundary frame conditions\n\nModels the slice of EVM `CALL` semantics that touches the caller's\nframe, and proves the frame conditions that downstream contract proofs\nneed to reason about external calls without quantifying over callee\nbytecode.\n\nPromoted from `Benchmark.Cases.ERC4337.EntryPointInvariant.EvmYulFrame`.\n\n## What this discharges\n\nBefore this module, every benchmark that touched external calls had to\nassume (or reproduce in their own file) the EVM-level frame condition\nthat external `CALL` cannot SSTORE the caller's slots and cannot write\nto caller memory outside the declared output buffer. That assumption is\ndocumented in `AXIOMS.md` under \"External Call Module\". This module\nmakes the assumption a *theorem* of `Verity.EVM`, parameterised over an\nabstract `CalleeResult` whose universal quantification over its\ninhabitants is equivalent to quantifying over arbitrary EVM callee\nbytecode.\n\n## Roadmap\n\nA subsequent PR will prove that this abstract `CallerFrame` /\n`CalleeResult` model is the projection of EvmYul's actual `CALL` opcode\nsemantics, closing the gap between this layer and the deeper EvmYul\ncorrectness theorems.\n-/\n\n/-- An EVM address (160-bit; we expose identity only). -/\nabbrev Address := Nat\n\n/-- The caller-side EVM frame at a `CALL` boundary. The four mutable\n sub-states the EVM exposes to a contract are modelled explicitly. -/\nstructure CallerFrame where\n thisAddress : Address\n memory : Nat → Uint256\n storageMap : Nat → Uint256\n transientStorage : Nat → Uint256\n returnDataBuf : Nat → Uint256\n\n/-- Everything an arbitrary callee can return to the caller across a\n `CALL` boundary. The callee's internal storage updates are scoped to\n its own address and so do not appear here — they cannot affect the\n caller's frame. Quantifying over inhabitants of this type is\n equivalent to quantifying over arbitrary EVM callee programs that\n produce any `(success, returndata)` pair. -/\nstructure CalleeResult where\n success : Uint256\n returnedData : Nat → Uint256\n\n/-- The portion of EVM `CALL` semantics that touches the caller's frame.\n\nBy the Yellow Paper, `CALL` to a target ≠ self with the caller's output\nbuffer `[outOff, outOff + outSize)` updates the caller's memory by\ncopying `outSize` words of the callee's returndata into that range,\nleaves storage and transient storage untouched, and writes the new\nreturndata buffer to the caller's `returnDataBuf`. -/\ndef applyCallToCaller\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n : CallerFrame :=\n { caller with\n memory := fun i =>\n if outOff ≤ i ∧ i < outOff + outSize then\n callee.returnedData (i - outOff)\n else\n caller.memory i\n returnDataBuf := callee.returnedData }\n\n/-! ## Single-CALL frame theorems -/\n\ntheorem external_calls_preserve_caller_transient_storage\n (caller : CallerFrame)\n (calls : List (Nat × Nat × CalleeResult))\n (slotIdx : Nat) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).transientStorage slotIdx =\n caller.transientStorage slotIdx := sorry\n\nend Verity.EVM.Frame\n"},"solution_file_content":{"kind":"string","value":"import Verity.EVM.Uint256\nimport Verity.EVM.MemoryModel\nimport Verity.Core.Uint256\n\nnamespace Verity.EVM.Frame\n\nopen Verity.Core (Uint256)\nopen Verity.EVM.MemoryModel\n\n/-!\n# EVM `CALL` boundary frame conditions\n\nModels the slice of EVM `CALL` semantics that touches the caller's\nframe, and proves the frame conditions that downstream contract proofs\nneed to reason about external calls without quantifying over callee\nbytecode.\n\nPromoted from `Benchmark.Cases.ERC4337.EntryPointInvariant.EvmYulFrame`.\n\n## What this discharges\n\nBefore this module, every benchmark that touched external calls had to\nassume (or reproduce in their own file) the EVM-level frame condition\nthat external `CALL` cannot SSTORE the caller's slots and cannot write\nto caller memory outside the declared output buffer. That assumption is\ndocumented in `AXIOMS.md` under \"External Call Module\". This module\nmakes the assumption a *theorem* of `Verity.EVM`, parameterised over an\nabstract `CalleeResult` whose universal quantification over its\ninhabitants is equivalent to quantifying over arbitrary EVM callee\nbytecode.\n\n## Roadmap\n\nA subsequent PR will prove that this abstract `CallerFrame` /\n`CalleeResult` model is the projection of EvmYul's actual `CALL` opcode\nsemantics, closing the gap between this layer and the deeper EvmYul\ncorrectness theorems.\n-/\n\n/-- An EVM address (160-bit; we expose identity only). -/\nabbrev Address := Nat\n\n/-- The caller-side EVM frame at a `CALL` boundary. The four mutable\n sub-states the EVM exposes to a contract are modelled explicitly. -/\nstructure CallerFrame where\n thisAddress : Address\n memory : Nat → Uint256\n storageMap : Nat → Uint256\n transientStorage : Nat → Uint256\n returnDataBuf : Nat → Uint256\n\n/-- Everything an arbitrary callee can return to the caller across a\n `CALL` boundary. The callee's internal storage updates are scoped to\n its own address and so do not appear here — they cannot affect the\n caller's frame. Quantifying over inhabitants of this type is\n equivalent to quantifying over arbitrary EVM callee programs that\n produce any `(success, returndata)` pair. -/\nstructure CalleeResult where\n success : Uint256\n returnedData : Nat → Uint256\n\n/-- The portion of EVM `CALL` semantics that touches the caller's frame.\n\nBy the Yellow Paper, `CALL` to a target ≠ self with the caller's output\nbuffer `[outOff, outOff + outSize)` updates the caller's memory by\ncopying `outSize` words of the callee's returndata into that range,\nleaves storage and transient storage untouched, and writes the new\nreturndata buffer to the caller's `returnDataBuf`. -/\ndef applyCallToCaller\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n : CallerFrame :=\n { caller with\n memory := fun i =>\n if outOff ≤ i ∧ i < outOff + outSize then\n callee.returnedData (i - outOff)\n else\n caller.memory i\n returnDataBuf := callee.returnedData }\n\n/-! ## Single-CALL frame theorems -/\n\ntheorem external_call_preserves_caller_transient_storage\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (slotIdx : Nat) :\n (applyCallToCaller caller outOff outSize callee).transientStorage slotIdx =\n caller.transientStorage slotIdx := by\n simp [applyCallToCaller]\n\ntheorem external_calls_preserve_caller_transient_storage\n (caller : CallerFrame)\n (calls : List (Nat × Nat × CalleeResult))\n (slotIdx : Nat) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).transientStorage slotIdx =\n caller.transientStorage slotIdx := by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n have hStep := external_call_preserves_caller_transient_storage\n caller c.1 c.2.1 c.2.2 slotIdx\n have := ih (applyCallToCaller caller c.1 c.2.1 c.2.2)\n simp [List.foldl]; rw [this, hStep]\n\nend Verity.EVM.Frame\n"},"solution_diff":{"kind":"string","value":"@@ -79,13 +79,27 @@\n \n /-! ## Single-CALL frame theorems -/\n \n+theorem external_call_preserves_caller_transient_storage\n+ (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n+ (slotIdx : Nat) :\n+ (applyCallToCaller caller outOff outSize callee).transientStorage slotIdx =\n+ caller.transientStorage slotIdx := by\n+ simp [applyCallToCaller]\n+\n theorem external_calls_preserve_caller_transient_storage\n (caller : CallerFrame)\n (calls : List (Nat × Nat × CalleeResult))\n (slotIdx : Nat) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).transientStorage slotIdx =\n- caller.transientStorage slotIdx := sorry\n+ caller.transientStorage slotIdx := by\n+ induction calls generalizing caller with\n+ | nil => rfl\n+ | cons c rest ih =>\n+ have hStep := external_call_preserves_caller_transient_storage\n+ caller c.1 c.2.1 c.2.2 slotIdx\n+ have := ih (applyCallToCaller caller c.1 c.2.1 c.2.2)\n+ simp [List.foldl]; rw [this, hStep]\n \n end Verity.EVM.Frame\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21387,"cells":{"task_id":{"kind":"string","value":"ablate_bd1f7089f857_3"},"challenge_id":{"kind":"string","value":"ce39bb8129d53b34"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Verity/EVM/Frame.lean"},"theory":{"kind":"string","value":"Frame"},"variant":{"kind":"number","value":3,"string":"3"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":4,"string":"4"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"external_calls_preserve_caller_memory_in_disjoint_region","depth":1,"n_commands":0,"n_lines":10,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n have hStep := external_call_preserves_caller_memory caller c.1 c.2.1 c.2.2\n regionLo regionHi (hAllDisj c (List.mem_cons_self ..)) i hLo hHi\n have hRest : ∀ d ∈ rest, d.1 + d.2.1 ≤ regionLo ∨ regionHi ≤ d.1 := by\n intro d hd; exact hAllDisj d (List.mem_cons_of_mem _ hd)\n have hIH := ih (applyCallToCaller caller c.1 c.2.1 c.2.2) hRest\n simp [List.foldl]; rw [hIH, hStep]","n_chars":488,"n_subproofs":3,"n_tactics":12,"cyclomatic":2,"n_automation":2,"n_rewrites":1,"n_structural":3,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"theorem_name\": \"external_calls_preserve_caller_memory_in_disjoint_region\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 10,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n induction calls generalizing caller with\\n | nil => rfl\\n | cons c rest ih =>\\n have hStep := external_call_preserves_caller_memory caller c.1 c.2.1 c.2.2\\n regionLo regionHi (hAllDisj c (List.mem_cons_self ..)) i hLo hHi\\n have hRest : ∀ d ∈ rest, d.1 + d.2.1 ≤ regionLo ∨ regionHi ≤ d.1 := by\\n intro d hd; exact hAllDisj d (List.mem_cons_of_mem _ hd)\\n have hIH := ih (applyCallToCaller caller c.1 c.2.1 c.2.2) hRest\\n simp [List.foldl]; rw [hIH, hStep]\",\n \"n_chars\": 488,\n \"n_subproofs\": 3,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"external_call_preserves_caller_memory","text":"/-- Headline form: caller-memory preservation under a disjoint output\n buffer. Composes directly with `MemoryModel.Disjoint`. -/\ntheorem external_call_preserves_caller_memory\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (regionLo regionHi : Nat)\n (hDisj : outOff + outSize ≤ regionLo ∨ regionHi ≤ outOff)\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n caller.memory i := by\n apply external_call_preserves_caller_memory_outside_output_buffer\n rintro ⟨h1, h2⟩\n rcases hDisj with h | h <;> omega\n\n/-! ## Iterated-CALL frame theorems -/\n\n","fan_in":1,"n_lines":16,"n_chars":669,"n_subproofs":0,"n_tactics":5,"cyclomatic":4,"n_automation":1,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"external_call_preserves_caller_memory\",\n \"text\": \"/-- Headline form: caller-memory preservation under a disjoint output\\n buffer. Composes directly with `MemoryModel.Disjoint`. -/\\ntheorem external_call_preserves_caller_memory\\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\\n (regionLo regionHi : Nat)\\n (hDisj : outOff + outSize ≤ regionLo ∨ regionHi ≤ outOff)\\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\\n (applyCallToCaller caller outOff outSize callee).memory i =\\n caller.memory i := by\\n apply external_call_preserves_caller_memory_outside_output_buffer\\n rintro ⟨h1, h2⟩\\n rcases hDisj with h | h <;> omega\\n\\n/-! ## Iterated-CALL frame theorems -/\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 16,\n \"n_chars\": 669,\n \"n_subproofs\": 0,\n \"n_tactics\": 5,\n \"cyclomatic\": 4,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"external_calls_preserve_caller_memory_in_disjoint_region","fan_in":0,"n_deps_direct":1,"n_deps_transitive":2,"n_lines":21,"n_chars":919,"n_subproofs":3,"n_tactics":12,"cyclomatic":2,"n_automation":2,"n_rewrites":1,"n_structural":3,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"external_calls_preserve_caller_memory_in_disjoint_region\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 2,\n \"n_lines\": 21,\n \"n_chars\": 919,\n \"n_subproofs\": 3,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":2,"string":"2"},"challenge_file_content":{"kind":"string","value":"import Verity.EVM.Uint256\nimport Verity.EVM.MemoryModel\nimport Verity.Core.Uint256\n\nnamespace Verity.EVM.Frame\n\nopen Verity.Core (Uint256)\nopen Verity.EVM.MemoryModel\n\n/-!\n# EVM `CALL` boundary frame conditions\n\nModels the slice of EVM `CALL` semantics that touches the caller's\nframe, and proves the frame conditions that downstream contract proofs\nneed to reason about external calls without quantifying over callee\nbytecode.\n\nPromoted from `Benchmark.Cases.ERC4337.EntryPointInvariant.EvmYulFrame`.\n\n## What this discharges\n\nBefore this module, every benchmark that touched external calls had to\nassume (or reproduce in their own file) the EVM-level frame condition\nthat external `CALL` cannot SSTORE the caller's slots and cannot write\nto caller memory outside the declared output buffer. That assumption is\ndocumented in `AXIOMS.md` under \"External Call Module\". This module\nmakes the assumption a *theorem* of `Verity.EVM`, parameterised over an\nabstract `CalleeResult` whose universal quantification over its\ninhabitants is equivalent to quantifying over arbitrary EVM callee\nbytecode.\n\n## Roadmap\n\nA subsequent PR will prove that this abstract `CallerFrame` /\n`CalleeResult` model is the projection of EvmYul's actual `CALL` opcode\nsemantics, closing the gap between this layer and the deeper EvmYul\ncorrectness theorems.\n-/\n\n/-- An EVM address (160-bit; we expose identity only). -/\nabbrev Address := Nat\n\n/-- The caller-side EVM frame at a `CALL` boundary. The four mutable\n sub-states the EVM exposes to a contract are modelled explicitly. -/\nstructure CallerFrame where\n thisAddress : Address\n memory : Nat → Uint256\n storageMap : Nat → Uint256\n transientStorage : Nat → Uint256\n returnDataBuf : Nat → Uint256\n\n/-- Everything an arbitrary callee can return to the caller across a\n `CALL` boundary. The callee's internal storage updates are scoped to\n its own address and so do not appear here — they cannot affect the\n caller's frame. Quantifying over inhabitants of this type is\n equivalent to quantifying over arbitrary EVM callee programs that\n produce any `(success, returndata)` pair. -/\nstructure CalleeResult where\n success : Uint256\n returnedData : Nat → Uint256\n\n/-- The portion of EVM `CALL` semantics that touches the caller's frame.\n\nBy the Yellow Paper, `CALL` to a target ≠ self with the caller's output\nbuffer `[outOff, outOff + outSize)` updates the caller's memory by\ncopying `outSize` words of the callee's returndata into that range,\nleaves storage and transient storage untouched, and writes the new\nreturndata buffer to the caller's `returnDataBuf`. -/\ndef applyCallToCaller\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n : CallerFrame :=\n { caller with\n memory := fun i =>\n if outOff ≤ i ∧ i < outOff + outSize then\n callee.returnedData (i - outOff)\n else\n caller.memory i\n returnDataBuf := callee.returnedData }\n\n/-! ## Single-CALL frame theorems -/\n\ntheorem external_call_preserves_caller_memory_outside_output_buffer\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (i : Nat) (hOutside : ¬ (outOff ≤ i ∧ i < outOff + outSize)) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n caller.memory i := by\n simp [applyCallToCaller, hOutside]\n\ntheorem external_calls_preserve_caller_memory_in_disjoint_region\n (caller : CallerFrame)\n (regionLo regionHi : Nat)\n (calls : List (Nat × Nat × CalleeResult))\n (hAllDisj : ∀ c ∈ calls,\n c.1 + c.2.1 ≤ regionLo ∨ regionHi ≤ c.1)\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).memory i =\n caller.memory i := sorry\n\nend Verity.EVM.Frame\n"},"solution_file_content":{"kind":"string","value":"import Verity.EVM.Uint256\nimport Verity.EVM.MemoryModel\nimport Verity.Core.Uint256\n\nnamespace Verity.EVM.Frame\n\nopen Verity.Core (Uint256)\nopen Verity.EVM.MemoryModel\n\n/-!\n# EVM `CALL` boundary frame conditions\n\nModels the slice of EVM `CALL` semantics that touches the caller's\nframe, and proves the frame conditions that downstream contract proofs\nneed to reason about external calls without quantifying over callee\nbytecode.\n\nPromoted from `Benchmark.Cases.ERC4337.EntryPointInvariant.EvmYulFrame`.\n\n## What this discharges\n\nBefore this module, every benchmark that touched external calls had to\nassume (or reproduce in their own file) the EVM-level frame condition\nthat external `CALL` cannot SSTORE the caller's slots and cannot write\nto caller memory outside the declared output buffer. That assumption is\ndocumented in `AXIOMS.md` under \"External Call Module\". This module\nmakes the assumption a *theorem* of `Verity.EVM`, parameterised over an\nabstract `CalleeResult` whose universal quantification over its\ninhabitants is equivalent to quantifying over arbitrary EVM callee\nbytecode.\n\n## Roadmap\n\nA subsequent PR will prove that this abstract `CallerFrame` /\n`CalleeResult` model is the projection of EvmYul's actual `CALL` opcode\nsemantics, closing the gap between this layer and the deeper EvmYul\ncorrectness theorems.\n-/\n\n/-- An EVM address (160-bit; we expose identity only). -/\nabbrev Address := Nat\n\n/-- The caller-side EVM frame at a `CALL` boundary. The four mutable\n sub-states the EVM exposes to a contract are modelled explicitly. -/\nstructure CallerFrame where\n thisAddress : Address\n memory : Nat → Uint256\n storageMap : Nat → Uint256\n transientStorage : Nat → Uint256\n returnDataBuf : Nat → Uint256\n\n/-- Everything an arbitrary callee can return to the caller across a\n `CALL` boundary. The callee's internal storage updates are scoped to\n its own address and so do not appear here — they cannot affect the\n caller's frame. Quantifying over inhabitants of this type is\n equivalent to quantifying over arbitrary EVM callee programs that\n produce any `(success, returndata)` pair. -/\nstructure CalleeResult where\n success : Uint256\n returnedData : Nat → Uint256\n\n/-- The portion of EVM `CALL` semantics that touches the caller's frame.\n\nBy the Yellow Paper, `CALL` to a target ≠ self with the caller's output\nbuffer `[outOff, outOff + outSize)` updates the caller's memory by\ncopying `outSize` words of the callee's returndata into that range,\nleaves storage and transient storage untouched, and writes the new\nreturndata buffer to the caller's `returnDataBuf`. -/\ndef applyCallToCaller\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n : CallerFrame :=\n { caller with\n memory := fun i =>\n if outOff ≤ i ∧ i < outOff + outSize then\n callee.returnedData (i - outOff)\n else\n caller.memory i\n returnDataBuf := callee.returnedData }\n\n/-! ## Single-CALL frame theorems -/\n\ntheorem external_call_preserves_caller_memory_outside_output_buffer\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (i : Nat) (hOutside : ¬ (outOff ≤ i ∧ i < outOff + outSize)) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n caller.memory i := by\n simp [applyCallToCaller, hOutside]\n\n/-- Headline form: caller-memory preservation under a disjoint output\n buffer. Composes directly with `MemoryModel.Disjoint`. -/\ntheorem external_call_preserves_caller_memory\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (regionLo regionHi : Nat)\n (hDisj : outOff + outSize ≤ regionLo ∨ regionHi ≤ outOff)\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n (applyCallToCaller caller outOff outSize callee).memory i =\n caller.memory i := by\n apply external_call_preserves_caller_memory_outside_output_buffer\n rintro ⟨h1, h2⟩\n rcases hDisj with h | h <;> omega\n\n/-! ## Iterated-CALL frame theorems -/\n\ntheorem external_calls_preserve_caller_memory_in_disjoint_region\n (caller : CallerFrame)\n (regionLo regionHi : Nat)\n (calls : List (Nat × Nat × CalleeResult))\n (hAllDisj : ∀ c ∈ calls,\n c.1 + c.2.1 ≤ regionLo ∨ regionHi ≤ c.1)\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).memory i =\n caller.memory i := by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n have hStep := external_call_preserves_caller_memory caller c.1 c.2.1 c.2.2\n regionLo regionHi (hAllDisj c (List.mem_cons_self ..)) i hLo hHi\n have hRest : ∀ d ∈ rest, d.1 + d.2.1 ≤ regionLo ∨ regionHi ≤ d.1 := by\n intro d hd; exact hAllDisj d (List.mem_cons_of_mem _ hd)\n have hIH := ih (applyCallToCaller caller c.1 c.2.1 c.2.2) hRest\n simp [List.foldl]; rw [hIH, hStep]\n\nend Verity.EVM.Frame\n"},"solution_diff":{"kind":"string","value":"@@ -86,6 +86,21 @@\n caller.memory i := by\n simp [applyCallToCaller, hOutside]\n \n+/-- Headline form: caller-memory preservation under a disjoint output\n+ buffer. Composes directly with `MemoryModel.Disjoint`. -/\n+theorem external_call_preserves_caller_memory\n+ (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n+ (regionLo regionHi : Nat)\n+ (hDisj : outOff + outSize ≤ regionLo ∨ regionHi ≤ outOff)\n+ (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n+ (applyCallToCaller caller outOff outSize callee).memory i =\n+ caller.memory i := by\n+ apply external_call_preserves_caller_memory_outside_output_buffer\n+ rintro ⟨h1, h2⟩\n+ rcases hDisj with h | h <;> omega\n+\n+/-! ## Iterated-CALL frame theorems -/\n+\n theorem external_calls_preserve_caller_memory_in_disjoint_region\n (caller : CallerFrame)\n (regionLo regionHi : Nat)\n@@ -95,7 +110,16 @@\n (i : Nat) (hLo : regionLo ≤ i) (hHi : i < regionHi) :\n (calls.foldl\n (fun s c => applyCallToCaller s c.1 c.2.1 c.2.2) caller).memory i =\n- caller.memory i := sorry\n+ caller.memory i := by\n+ induction calls generalizing caller with\n+ | nil => rfl\n+ | cons c rest ih =>\n+ have hStep := external_call_preserves_caller_memory caller c.1 c.2.1 c.2.2\n+ regionLo regionHi (hAllDisj c (List.mem_cons_self ..)) i hLo hHi\n+ have hRest : ∀ d ∈ rest, d.1 + d.2.1 ≤ regionLo ∨ regionHi ≤ d.1 := by\n+ intro d hd; exact hAllDisj d (List.mem_cons_of_mem _ hd)\n+ have hIH := ih (applyCallToCaller caller c.1 c.2.1 c.2.2) hRest\n+ simp [List.foldl]; rw [hIH, hStep]\n \n end Verity.EVM.Frame\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21388,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_0"},"challenge_id":{"kind":"string","value":"70cfd87882fb4b8b"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":0,"string":"0"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":1,"string":"1"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileGuardedFunctionSpec_eq_of_none","depth":1,"n_commands":0,"n_lines":8,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]","n_chars":326,"n_subproofs":0,"n_tactics":8,"cyclomatic":2,"n_automation":2,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"compileGuardedFunctionSpec_eq_of_none\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 8,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n unfold compileGuardedFunctionSpec\\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\\n (targetFork := .cancun) internalFunctions with\\n | error err => simp [bind, Except.bind]\\n | ok irFn =>\\n simp [bind, Except.bind,\\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\",\n \"n_chars\": 326,\n \"n_subproofs\": 0,\n \"n_tactics\": 8,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"attachNonReentrantGuard_eq_of_none","text":"/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\n","fan_in":1,"n_lines":10,"n_chars":509,"n_subproofs":0,"n_tactics":2,"cyclomatic":1,"n_automation":1,"n_rewrites":0,"n_structural":0,"automation_only":true,"max_nesting":2}],"string":"[\n {\n \"name\": \"attachNonReentrantGuard_eq_of_none\",\n \"text\": \"/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\\nguarded per-function compile in `compileValidatedCore` collapses to the plain\\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\\ntheorem attachNonReentrantGuard_eq_of_none\\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\\n (hnone : spec.nonReentrantLock = none) :\\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\\n\\n\",\n \"fan_in\": 1,\n \"n_lines\": 10,\n \"n_chars\": 509,\n \"n_subproofs\": 0,\n \"n_tactics\": 2,\n \"cyclomatic\": 1,\n \"n_automation\": 1,\n \"n_rewrites\": 0,\n \"n_structural\": 0,\n \"automation_only\": true,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compileGuardedFunctionSpec_eq_of_none","fan_in":0,"n_deps_direct":1,"n_deps_transitive":1,"n_lines":17,"n_chars":821,"n_subproofs":0,"n_tactics":8,"cyclomatic":2,"n_automation":2,"n_rewrites":1,"n_structural":1,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"compileGuardedFunctionSpec_eq_of_none\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 1,\n \"n_lines\": 17,\n \"n_chars\": 821,\n \"n_subproofs\": 0,\n \"n_tactics\": 8,\n \"cyclomatic\": 2,\n \"n_automation\": 2,\n \"n_rewrites\": 1,\n \"n_structural\": 1,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":1,"string":"1"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn => sorry\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -9,6 +9,15 @@\n \n namespace ContractShape\n \n+/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\n+guarded per-function compile in `compileValidatedCore` collapses to the plain\n+`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\n+theorem attachNonReentrantGuard_eq_of_none\n+ (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n+ (hnone : spec.nonReentrantLock = none) :\n+ attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n+ simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n+\n theorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n@@ -21,7 +30,9 @@\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n- | ok irFn => sorry\n+ | ok irFn =>\n+ simp [bind, Except.bind,\n+ attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n \n theorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21389,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_1"},"challenge_id":{"kind":"string","value":"a8a317099699e124"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":1,"string":"1"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compileValidatedCore_ok_yields_compiled_functions","fan_in":1,"n_deps_direct":4,"n_deps_transitive":4,"n_lines":59,"n_chars":2702,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16}],"string":"[\n {\n \"name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"fan_in\": 1,\n \"n_deps_direct\": 4,\n \"n_deps_transitive\": 4,\n \"n_lines\": 59,\n \"n_chars\": 2702,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":4,"string":"4"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\nprivate theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n entries irFns := by\n intro entries\n induction entries with\n | nil =>\n intro irFns hmap\n cases hmap\n simp\n | cons entry entries ih =>\n intro irFns hmap\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n cases hmap\n · rcases htail : List.mapM\n (fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n exact List.Forall₂.cons hstep (ih _ htail)\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_compiled_functions\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := sorry\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\nprivate theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n entries irFns := by\n intro entries\n induction entries with\n | nil =>\n intro irFns hmap\n cases hmap\n simp\n | cons entry entries ih =>\n intro irFns hmap\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n cases hmap\n · rcases htail : List.mapM\n (fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n exact List.Forall₂.cons hstep (ih _ htail)\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_compiled_functions\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -103,6 +103,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -133,7 +143,53 @@\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n- ir.functions := sorry\n+ ir.functions := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ unfold compileValidatedCore at hcore\n+ rw [hSupported.normalizedFields,\n+ hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n+ hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · simp [hmap] at hcore\n+ simp [hSupported.surface.noTemplateIntrinsics] at hcore\n+ rcases hctor :\n+ compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n+ · simp [hctor] at hcore\n+ cases hcore\n+ · simp [hctor] at hcore\n+ have hfunctions : ir.functions = irFns := by\n+ injection hcore with hir\n+ cases hir\n+ rfl\n+ have hcompiled :\n+ List.Forall₂\n+ (fun (entry : FunctionSpec × Nat) irFn =>\n+ compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n+ irFns :=\n+ by\n+ simpa [hSupported.noEvents, hSupported.noErrors] using\n+ (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n+ simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n+ hfunctions] using hcompiled\n \n end ContractShape\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21390,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_2"},"challenge_id":{"kind":"string","value":"9d4d6462ae1b3bc1"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":2,"string":"2"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compileValidatedCore_ok_yields_internalFunctions_nil","fan_in":1,"n_deps_direct":3,"n_deps_transitive":3,"n_lines":50,"n_chars":2591,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"fan_in\": 1,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 3,\n \"n_lines\": 50,\n \"n_chars\": 2591,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_internalFunctions_nil\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.internalFunctions = [] := sorry\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_internalFunctions_nil\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.internalFunctions = [] := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -72,6 +72,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -98,7 +108,48 @@\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n- ir.internalFunctions = [] := sorry\n+ ir.internalFunctions = [] := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ have harray : contractUsesArrayElement model = false :=\n+ hSupported.contractUsesArrayElement_eq_false\n+ have hstorageArray : contractUsesStorageArrayElement model = false :=\n+ hSupported.contractUsesStorageArrayElement_eq_false\n+ have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n+ hSupported.contractUsesDynamicBytesEq_eq_false\n+ have hmulDiv512 : contractUsesMulDiv512 model = false :=\n+ hSupported.contractUsesMulDiv512_eq_false\n+ have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n+ hSupported.contractUsesParamDynamicHeadWord_eq_false\n+ unfold compileValidatedCore at hcore\n+ rw [hSupported.normalizedFields, hfallback, hreceive,\n+ contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n+ hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n+ hSupported.noCheckedArithmetic,\n+ hnoInternalFns, hSupported.noAdtTypes] at hcore\n+ simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n+ simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · rcases hctor :\n+ compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n+ cases hcore\n+ rfl\n \n end ContractShape\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21391,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_3"},"challenge_id":{"kind":"string","value":"0b55f116f61022bc"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":3,"string":"3"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compileValidatedCore_ok_yields_deploy_compileConstructor","fan_in":1,"n_deps_direct":3,"n_deps_transitive":3,"n_lines":42,"n_chars":1921,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"fan_in\": 1,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 3,\n \"n_lines\": 42,\n \"n_chars\": 1921,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_deploy_compileConstructor\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n compileConstructor model.fields model.events model.errors [] model.constructor =\n Except.ok ir.deploy := sorry\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_deploy_compileConstructor\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n compileConstructor model.fields model.events model.errors [] model.constructor =\n Except.ok ir.deploy := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -72,6 +72,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -99,7 +109,39 @@\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n compileConstructor model.fields model.events model.errors [] model.constructor =\n- Except.ok ir.deploy := sorry\n+ Except.ok ir.deploy := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ unfold compileValidatedCore at hcore\n+ rw [hSupported.normalizedFields,\n+ hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n+ hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · simp [hmap] at hcore\n+ simp [hSupported.surface.noTemplateIntrinsics] at hcore\n+ rcases hctor :\n+ compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n+ · simp [hctor] at hcore\n+ cases hcore\n+ · simp [hctor] at hcore\n+ cases hcore\n+ simpa [hSupported.noEvents, hSupported.noErrors] using hctor\n \n end ContractShape\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21392,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_4"},"challenge_id":{"kind":"string","value":"7ef0bef0ddf0d047"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":4,"string":"4"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","fan_in":1,"n_deps_direct":3,"n_deps_transitive":3,"n_lines":39,"n_chars":1991,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"fan_in\": 1,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 3,\n \"n_lines\": 39,\n \"n_chars\": 1991,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_noFallbackEntrypoint\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.fallbackEntrypoint = none := sorry\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_noFallbackEntrypoint\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.fallbackEntrypoint = none := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -72,6 +72,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -98,7 +108,37 @@\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n- ir.fallbackEntrypoint = none := sorry\n+ ir.fallbackEntrypoint = none := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ unfold compileValidatedCore at hcore\n+ rw [hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · rcases hctor :\n+ compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n+ cases hcore\n+ rfl\n \n end ContractShape\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21393,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_5"},"challenge_id":{"kind":"string","value":"80f600c95a01e280"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":5,"string":"5"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","fan_in":1,"n_deps_direct":3,"n_deps_transitive":3,"n_lines":39,"n_chars":1989,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"fan_in\": 1,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 3,\n \"n_lines\": 39,\n \"n_chars\": 1989,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_noReceiveEntrypoint\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.receiveEntrypoint = none := sorry\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_noReceiveEntrypoint\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.receiveEntrypoint = none := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -72,6 +72,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -98,7 +108,37 @@\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n- ir.receiveEntrypoint = none := sorry\n+ ir.receiveEntrypoint = none := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ unfold compileValidatedCore at hcore\n+ rw [hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · rcases hctor :\n+ compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n+ cases hcore\n+ rfl\n \n end ContractShape\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21394,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_6"},"challenge_id":{"kind":"string","value":"f3d2f5d9dc479255"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":6,"string":"6"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compile_ok_yields_compiled_functions","fan_in":0,"n_deps_direct":1,"n_deps_transitive":5,"n_lines":24,"n_chars":911,"n_subproofs":0,"n_tactics":12,"cyclomatic":2,"n_automation":3,"n_rewrites":1,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compile_ok_yields_compiled_functions\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 5,\n \"n_lines\": 24,\n \"n_chars\": 911,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 3,\n \"n_rewrites\": 1,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":5,"string":"5"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\nprivate theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n entries irFns := by\n intro entries\n induction entries with\n | nil =>\n intro irFns hmap\n cases hmap\n simp\n | cons entry entries ih =>\n intro irFns hmap\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n cases hmap\n · rcases htail : List.mapM\n (fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n exact List.Forall₂.cons hstep (ih _ htail)\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_compiled_functions\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := sorry\n\ntheorem compile_ok_yields_compiled_functions\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_compiled_functions\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\nprivate theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n entries irFns := by\n intro entries\n induction entries with\n | nil =>\n intro irFns hmap\n cases hmap\n simp\n | cons entry entries ih =>\n intro irFns hmap\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n cases hmap\n · rcases htail : List.mapM\n (fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n exact List.Forall₂.cons hstep (ih _ htail)\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_compiled_functions\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled\n\ntheorem compile_ok_yields_compiled_functions\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_compiled_functions\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -103,6 +103,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -133,7 +143,53 @@\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n- ir.functions := sorry\n+ ir.functions := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ unfold compileValidatedCore at hcore\n+ rw [hSupported.normalizedFields,\n+ hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n+ hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · simp [hmap] at hcore\n+ simp [hSupported.surface.noTemplateIntrinsics] at hcore\n+ rcases hctor :\n+ compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n+ · simp [hctor] at hcore\n+ cases hcore\n+ · simp [hctor] at hcore\n+ have hfunctions : ir.functions = irFns := by\n+ injection hcore with hir\n+ cases hir\n+ rfl\n+ have hcompiled :\n+ List.Forall₂\n+ (fun (entry : FunctionSpec × Nat) irFn =>\n+ compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n+ irFns :=\n+ by\n+ simpa [hSupported.noEvents, hSupported.noErrors] using\n+ (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n+ simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n+ hfunctions] using hcompiled\n \n theorem compile_ok_yields_compiled_functions\n (model : CompilationModel)\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21395,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_7"},"challenge_id":{"kind":"string","value":"7e427c333e3e520e"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":7,"string":"7"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":6,"string":"6"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions_with_scalar_events","depth":1,"n_commands":0,"n_lines":34,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback := pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.surface.noFallback\n have hreceive := pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.surface.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n hSupported.noInternalFunctions\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hSupported.noAdtTypes, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events [] [] [] _\n (supportedSpecWithScalarEvents_entries_lock_free hSupported)] at hcore\n rcases hmap : ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields model.events [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled := compiled_functions_forall₂_of_mapM_ok\n model.fields model.events [] _ _ hmap\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions, hSupported.noErrors] using hcompiled","n_chars":1705,"n_subproofs":5,"n_tactics":34,"cyclomatic":5,"n_automation":9,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 34,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback := pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.surface.noFallback\\n have hreceive := pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.surface.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\\n hSupported.noInternalFunctions\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hSupported.noAdtTypes, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events [] [] [] _\\n (supportedSpecWithScalarEvents_entries_lock_free hSupported)] at hcore\\n rcases hmap : ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields model.events [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled := compiled_functions_forall₂_of_mapM_ok\\n model.fields model.events [] _ _ hmap\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions, hSupported.noErrors] using hcompiled\",\n \"n_chars\": 1705,\n \"n_subproofs\": 5,\n \"n_tactics\": 34,\n \"cyclomatic\": 5,\n \"n_automation\": 9,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"pickUniqueFunctionByName_eq_ok_none_of_absent","text":"private theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n","fan_in":6,"n_lines":20,"n_chars":683,"n_subproofs":4,"n_tactics":15,"cyclomatic":2,"n_automation":6,"n_rewrites":0,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"name\": \"pickUniqueFunctionByName_eq_ok_none_of_absent\",\n \"text\": \"private theorem pickUniqueFunctionByName_eq_ok_none_of_absent\\n (name : String) (funcs : List FunctionSpec)\\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\\n pickUniqueFunctionByName name funcs = Except.ok none := by\\n induction funcs with\\n | nil =>\\n rfl\\n | cons fn rest ih =>\\n have hfn : (fn.name == name) = false := by\\n by_cases heq : fn.name = name\\n · have habs := habsent fn (by simp)\\n simp [heq] at habs\\n · simp [heq]\\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\\n intro fn' hmem\\n exact habsent fn' (by simp [hmem])\\n have ih' := ih hrest\\n simpa [pickUniqueFunctionByName, hfn] using ih'\\n\\n\",\n \"fan_in\": 6,\n \"n_lines\": 20,\n \"n_chars\": 683,\n \"n_subproofs\": 4,\n \"n_tactics\": 15,\n \"cyclomatic\": 2,\n \"n_automation\": 6,\n \"n_rewrites\": 0,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compileValidatedCore_ok_yields_compiled_functions_with_scalar_events","fan_in":1,"n_deps_direct":3,"n_deps_transitive":3,"n_lines":46,"n_chars":2236,"n_subproofs":5,"n_tactics":34,"cyclomatic":5,"n_automation":9,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"name\": \"compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\",\n \"fan_in\": 1,\n \"n_deps_direct\": 3,\n \"n_deps_transitive\": 3,\n \"n_lines\": 46,\n \"n_chars\": 2236,\n \"n_subproofs\": 5,\n \"n_tactics\": 34,\n \"cyclomatic\": 5,\n \"n_automation\": 9,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":3,"string":"3"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n entries irFns := by\n intro entries\n induction entries with\n | nil =>\n intro irFns hmap\n cases hmap\n simp\n | cons entry entries ih =>\n intro irFns hmap\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n cases hmap\n · rcases htail : List.mapM\n (fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n exact List.Forall₂.cons hstep (ih _ htail)\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpecWithScalarEvents_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpecWithScalarEvents model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpecWithScalarEvents model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := sorry\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\nprivate theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n entries irFns := by\n intro entries\n induction entries with\n | nil =>\n intro irFns hmap\n cases hmap\n simp\n | cons entry entries ih =>\n intro irFns hmap\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n cases hmap\n · rcases htail : List.mapM\n (fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n exact List.Forall₂.cons hstep (ih _ htail)\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpecWithScalarEvents_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpecWithScalarEvents model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpecWithScalarEvents model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := by\n have hfallback := pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.surface.noFallback\n have hreceive := pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.surface.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n hSupported.noInternalFunctions\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hSupported.noAdtTypes, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events [] [] [] _\n (supportedSpecWithScalarEvents_entries_lock_free hSupported)] at hcore\n rcases hmap : ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields model.events [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled := compiled_functions_forall₂_of_mapM_ok\n model.fields model.events [] _ _ hmap\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions, hSupported.noErrors] using hcompiled\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -9,6 +9,25 @@\n \n namespace ContractShape\n \n+private theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n+ (name : String) (funcs : List FunctionSpec)\n+ (habsent : ∀ fn ∈ funcs, fn.name != name) :\n+ pickUniqueFunctionByName name funcs = Except.ok none := by\n+ induction funcs with\n+ | nil =>\n+ rfl\n+ | cons fn rest ih =>\n+ have hfn : (fn.name == name) = false := by\n+ by_cases heq : fn.name = name\n+ · have habs := habsent fn (by simp)\n+ simp [heq] at habs\n+ · simp [heq]\n+ have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n+ intro fn' hmem\n+ exact habsent fn' (by simp [hmem])\n+ have ih' := ih hrest\n+ simpa [pickUniqueFunctionByName, hfn] using ih'\n+\n private theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n@@ -116,7 +135,40 @@\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n- ir.functions := sorry\n+ ir.functions := by\n+ have hfallback := pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.surface.noFallback\n+ have hreceive := pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.surface.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n+ hSupported.noInternalFunctions\n+ unfold compileValidatedCore at hcore\n+ rw [hSupported.normalizedFields, hSupported.noAdtTypes, hSupported.noErrors,\n+ hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq model.fields model.events [] [] [] _\n+ (supportedSpecWithScalarEvents_entries_lock_free hSupported)] at hcore\n+ rcases hmap : ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec model.fields model.events [] [] x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · simp [hmap] at hcore\n+ simp [hSupported.surface.noTemplateIntrinsics] at hcore\n+ rcases hctor :\n+ compileConstructor model.fields model.events [] [] model.constructor with _ | deployStmts\n+ · simp [hctor] at hcore\n+ cases hcore\n+ · simp [hctor] at hcore\n+ have hfunctions : ir.functions = irFns := by\n+ injection hcore with hir\n+ cases hir\n+ rfl\n+ have hcompiled := compiled_functions_forall₂_of_mapM_ok\n+ model.fields model.events [] _ _ hmap\n+ simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n+ hfunctions, hSupported.noErrors] using hcompiled\n \n end ContractShape\n \n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21396,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_8"},"challenge_id":{"kind":"string","value":"e04b168bca979f39"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":8,"string":"8"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":2,"string":"2"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions_with_scalar_events","depth":1,"n_commands":0,"n_lines":34,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback := pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.surface.noFallback\n have hreceive := pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.surface.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n hSupported.noInternalFunctions\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hSupported.noAdtTypes, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events [] [] [] _\n (supportedSpecWithScalarEvents_entries_lock_free hSupported)] at hcore\n rcases hmap : ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields model.events [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled := compiled_functions_forall₂_of_mapM_ok\n model.fields model.events [] _ _ hmap\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions, hSupported.noErrors] using hcompiled","n_chars":1705,"n_subproofs":5,"n_tactics":34,"cyclomatic":5,"n_automation":9,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":8}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 34,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback := pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.surface.noFallback\\n have hreceive := pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.surface.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\\n hSupported.noInternalFunctions\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hSupported.noAdtTypes, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events [] [] [] _\\n (supportedSpecWithScalarEvents_entries_lock_free hSupported)] at hcore\\n rcases hmap : ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields model.events [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled := compiled_functions_forall₂_of_mapM_ok\\n model.fields model.events [] _ _ hmap\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions, hSupported.noErrors] using hcompiled\",\n \"n_chars\": 1705,\n \"n_subproofs\": 5,\n \"n_tactics\": 34,\n \"cyclomatic\": 5,\n \"n_automation\": 9,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 8\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"compiled_functions_forall₂_of_mapM_ok","text":"private theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n entries irFns := by\n intro entries\n induction entries with\n | nil =>\n intro irFns hmap\n cases hmap\n simp\n | cons entry entries ih =>\n intro irFns hmap\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n cases hmap\n · rcases htail : List.mapM\n (fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n exact List.Forall₂.cons hstep (ih _ htail)\n\n","fan_in":2,"n_lines":32,"n_chars":1313,"n_subproofs":0,"n_tactics":20,"cyclomatic":8,"n_automation":4,"n_rewrites":0,"n_structural":11,"automation_only":false,"max_nesting":14}],"string":"[\n {\n \"name\": \"compiled_functions_forall₂_of_mapM_ok\",\n \"text\": \"private theorem compiled_functions_forall₂_of_mapM_ok\\n (fields : List Field)\\n (events : List EventDef)\\n (errors : List ErrorDef) :\\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\\n entries irFns := by\\n intro entries\\n induction entries with\\n | nil =>\\n intro irFns hmap\\n cases hmap\\n simp\\n | cons entry entries ih =>\\n intro irFns hmap\\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\\n cases hmap\\n · rcases htail : List.mapM\\n (fun (entry : FunctionSpec × Nat) =>\\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\\n cases hmap\\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\\n cases hmap\\n exact List.Forall₂.cons hstep (ih _ htail)\\n\\n\",\n \"fan_in\": 2,\n \"n_lines\": 32,\n \"n_chars\": 1313,\n \"n_subproofs\": 0,\n \"n_tactics\": 20,\n \"cyclomatic\": 8,\n \"n_automation\": 4,\n \"n_rewrites\": 0,\n \"n_structural\": 11,\n \"automation_only\": false,\n \"max_nesting\": 14\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compile_ok_yields_compiled_functions_with_scalar_events","fan_in":0,"n_deps_direct":1,"n_deps_transitive":4,"n_lines":24,"n_chars":965,"n_subproofs":0,"n_tactics":12,"cyclomatic":2,"n_automation":3,"n_rewrites":1,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compile_ok_yields_compiled_functions_with_scalar_events\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 4,\n \"n_lines\": 24,\n \"n_chars\": 965,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 3,\n \"n_rewrites\": 1,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":4,"string":"4"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpecWithScalarEvents_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpecWithScalarEvents model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpecWithScalarEvents model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := sorry\n\ntheorem compile_ok_yields_compiled_functions_with_scalar_events\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpecWithScalarEvents model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\nprivate theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n entries irFns := by\n intro entries\n induction entries with\n | nil =>\n intro irFns hmap\n cases hmap\n simp\n | cons entry entries ih =>\n intro irFns hmap\n rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n cases hmap\n · rcases htail : List.mapM\n (fun (entry : FunctionSpec × Nat) =>\n compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n cases hmap\n exact List.Forall₂.cons hstep (ih _ htail)\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpecWithScalarEvents_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpecWithScalarEvents model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpecWithScalarEvents model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := by\n have hfallback := pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.surface.noFallback\n have hreceive := pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.surface.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n hSupported.noInternalFunctions\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hSupported.noAdtTypes, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events [] [] [] _\n (supportedSpecWithScalarEvents_entries_lock_free hSupported)] at hcore\n rcases hmap : ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields model.events [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled := compiled_functions_forall₂_of_mapM_ok\n model.fields model.events [] _ _ hmap\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions, hSupported.noErrors] using hcompiled\n\ntheorem compile_ok_yields_compiled_functions_with_scalar_events\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpecWithScalarEvents model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n List.Forall₂\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n ir.functions := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_compiled_functions_with_scalar_events\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -28,6 +28,37 @@\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n \n+private theorem compiled_functions_forall₂_of_mapM_ok\n+ (fields : List Field)\n+ (events : List EventDef)\n+ (errors : List ErrorDef) :\n+ ∀ (entries : List (FunctionSpec × Nat)) irFns,\n+ (entries.mapM fun (entry : FunctionSpec × Nat) =>\n+ compileFunctionSpec fields events errors [] entry.2 entry.1) = Except.ok irFns →\n+ List.Forall₂\n+ (fun (entry : FunctionSpec × Nat) irFn =>\n+ compileFunctionSpec fields events errors [] entry.2 entry.1 = Except.ok irFn)\n+ entries irFns := by\n+ intro entries\n+ induction entries with\n+ | nil =>\n+ intro irFns hmap\n+ cases hmap\n+ simp\n+ | cons entry entries ih =>\n+ intro irFns hmap\n+ rcases hstep : compileFunctionSpec fields events errors [] entry.2 entry.1 with _ | irFn\n+ · simp only [List.mapM_cons, hstep, bind, Except.bind] at hmap\n+ cases hmap\n+ · rcases htail : List.mapM\n+ (fun (entry : FunctionSpec × Nat) =>\n+ compileFunctionSpec fields events errors [] entry.2 entry.1) entries with _ | irFnsTail\n+ · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n+ cases hmap\n+ · simp only [List.mapM_cons, hstep, htail, bind, Except.bind] at hmap\n+ cases hmap\n+ exact List.Forall₂.cons hstep (ih _ htail)\n+\n /-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\n guarded per-function compile in `compileValidatedCore` collapses to the plain\n `compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\n@@ -104,7 +135,40 @@\n (fun entry irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n (SourceSemantics.selectorFunctionPairs model selectors)\n- ir.functions := sorry\n+ ir.functions := by\n+ have hfallback := pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.surface.noFallback\n+ have hreceive := pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.surface.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n+ hSupported.noInternalFunctions\n+ unfold compileValidatedCore at hcore\n+ rw [hSupported.normalizedFields, hSupported.noAdtTypes, hSupported.noErrors,\n+ hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq model.fields model.events [] [] [] _\n+ (supportedSpecWithScalarEvents_entries_lock_free hSupported)] at hcore\n+ rcases hmap : ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec model.fields model.events [] [] x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · simp [hmap] at hcore\n+ simp [hSupported.surface.noTemplateIntrinsics] at hcore\n+ rcases hctor :\n+ compileConstructor model.fields model.events [] [] model.constructor with _ | deployStmts\n+ · simp [hctor] at hcore\n+ cases hcore\n+ · simp [hctor] at hcore\n+ have hfunctions : ir.functions = irFns := by\n+ injection hcore with hir\n+ cases hir\n+ rfl\n+ have hcompiled := compiled_functions_forall₂_of_mapM_ok\n+ model.fields model.events [] _ _ hmap\n+ simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n+ hfunctions, hSupported.noErrors] using hcompiled\n \n theorem compile_ok_yields_compiled_functions_with_scalar_events\n (model : CompilationModel)\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21397,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_9"},"challenge_id":{"kind":"string","value":"7c0c1d3c246865f8"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":9,"string":"9"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compile_ok_yields_internalFunctions_nil","fan_in":0,"n_deps_direct":1,"n_deps_transitive":4,"n_lines":20,"n_chars":718,"n_subproofs":0,"n_tactics":12,"cyclomatic":2,"n_automation":3,"n_rewrites":1,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compile_ok_yields_internalFunctions_nil\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 4,\n \"n_lines\": 20,\n \"n_chars\": 718,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 3,\n \"n_rewrites\": 1,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":4,"string":"4"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_internalFunctions_nil\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.internalFunctions = [] := sorry\n\ntheorem compile_ok_yields_internalFunctions_nil\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n ir.internalFunctions = [] := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_internalFunctions_nil\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_internalFunctions_nil\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.internalFunctions = [] := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl\n\ntheorem compile_ok_yields_internalFunctions_nil\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n ir.internalFunctions = [] := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_internalFunctions_nil\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -72,6 +72,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -98,7 +108,48 @@\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n- ir.internalFunctions = [] := sorry\n+ ir.internalFunctions = [] := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ have harray : contractUsesArrayElement model = false :=\n+ hSupported.contractUsesArrayElement_eq_false\n+ have hstorageArray : contractUsesStorageArrayElement model = false :=\n+ hSupported.contractUsesStorageArrayElement_eq_false\n+ have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n+ hSupported.contractUsesDynamicBytesEq_eq_false\n+ have hmulDiv512 : contractUsesMulDiv512 model = false :=\n+ hSupported.contractUsesMulDiv512_eq_false\n+ have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n+ hSupported.contractUsesParamDynamicHeadWord_eq_false\n+ unfold compileValidatedCore at hcore\n+ rw [hSupported.normalizedFields, hfallback, hreceive,\n+ contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n+ hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n+ hSupported.noCheckedArithmetic,\n+ hnoInternalFns, hSupported.noAdtTypes] at hcore\n+ simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n+ simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · rcases hctor :\n+ compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n+ cases hcore\n+ rfl\n \n theorem compile_ok_yields_internalFunctions_nil\n (model : CompilationModel)\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21398,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_10"},"challenge_id":{"kind":"string","value":"aa2edda7964b2633"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":10,"string":"10"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compile_ok_yields_deploy_compileConstructor","fan_in":0,"n_deps_direct":1,"n_deps_transitive":4,"n_lines":21,"n_chars":807,"n_subproofs":0,"n_tactics":12,"cyclomatic":2,"n_automation":3,"n_rewrites":1,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compile_ok_yields_deploy_compileConstructor\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 4,\n \"n_lines\": 21,\n \"n_chars\": 807,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 3,\n \"n_rewrites\": 1,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":4,"string":"4"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_deploy_compileConstructor\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n compileConstructor model.fields model.events model.errors [] model.constructor =\n Except.ok ir.deploy := sorry\n\ntheorem compile_ok_yields_deploy_compileConstructor\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n compileConstructor model.fields model.events model.errors [] model.constructor =\n Except.ok ir.deploy := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_deploy_compileConstructor\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_deploy_compileConstructor\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n compileConstructor model.fields model.events model.errors [] model.constructor =\n Except.ok ir.deploy := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\n\ntheorem compile_ok_yields_deploy_compileConstructor\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n compileConstructor model.fields model.events model.errors [] model.constructor =\n Except.ok ir.deploy := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_deploy_compileConstructor\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -72,6 +72,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -99,7 +109,39 @@\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n compileConstructor model.fields model.events model.errors [] model.constructor =\n- Except.ok ir.deploy := sorry\n+ Except.ok ir.deploy := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ unfold compileValidatedCore at hcore\n+ rw [hSupported.normalizedFields,\n+ hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n+ hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · simp [hmap] at hcore\n+ simp [hSupported.surface.noTemplateIntrinsics] at hcore\n+ rcases hctor :\n+ compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n+ · simp [hctor] at hcore\n+ cases hcore\n+ · simp [hctor] at hcore\n+ cases hcore\n+ simpa [hSupported.noEvents, hSupported.noErrors] using hctor\n \n theorem compile_ok_yields_deploy_compileConstructor\n (model : CompilationModel)\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}},{"rowIdx":21399,"cells":{"task_id":{"kind":"string","value":"ablate_0b77e08220fe_11"},"challenge_id":{"kind":"string","value":"925ec05cd79bcfec"},"proof_assistant":{"kind":"string","value":"lean"},"session":{"kind":"string","value":"lean"},"repo":{"kind":"string","value":"github.com/lfglabs-dev/verity"},"revision":{"kind":"string","value":"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978"},"file_path":{"kind":"string","value":"Compiler/Proofs/IRGeneration/ContractShape.lean"},"theory":{"kind":"string","value":"ContractShape"},"variant":{"kind":"number","value":11,"string":"11"},"challenge_type":{"kind":"string","value":"lemma_delete"},"difficulty":{"kind":"null"},"count":{"kind":"null"},"by_centrality":{"kind":"bool","value":false,"string":"false"},"ablation_prob":{"kind":"number","value":0.5,"string":"0.5"},"min_depth":{"kind":"number","value":1,"string":"1"},"max_depth":{"kind":"number","value":1,"string":"1"},"leaves_only":{"kind":"bool","value":false,"string":"false"},"min_size":{"kind":"number","value":0,"string":"0"},"max_size":{"kind":"string","value":"inf"},"min_centrality":{"kind":"number","value":0,"string":"0"},"max_centrality":{"kind":"string","value":"inf"},"seed":{"kind":"number","value":42,"string":"42"},"n_proofs":{"kind":"number","value":12,"string":"12"},"n_ablated":{"kind":"number","value":5,"string":"5"},"holes_filled":{"kind":"list like","value":[{"theorem_name":"compileValidatedCore_ok_yields_compiled_functions","depth":1,"n_commands":0,"n_lines":47,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n have hfunctions : ir.functions = irFns := by\n injection hcore with hir\n cases hir\n rfl\n have hcompiled :\n List.Forall₂\n (fun (entry : FunctionSpec × Nat) irFn =>\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\n irFns :=\n by\n simpa [hSupported.noEvents, hSupported.noErrors] using\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\n hfunctions] using hcompiled","n_chars":2206,"n_subproofs":5,"n_tactics":47,"cyclomatic":5,"n_automation":10,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":16},{"theorem_name":"compileValidatedCore_ok_yields_internalFunctions_nil","depth":1,"n_commands":0,"n_lines":42,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n have harray : contractUsesArrayElement model = false :=\n hSupported.contractUsesArrayElement_eq_false\n have hstorageArray : contractUsesStorageArrayElement model = false :=\n hSupported.contractUsesStorageArrayElement_eq_false\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\n hSupported.contractUsesDynamicBytesEq_eq_false\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\n hSupported.contractUsesMulDiv512_eq_false\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\n hSupported.contractUsesParamDynamicHeadWord_eq_false\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields, hfallback, hreceive,\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\n hSupported.noCheckedArithmetic,\n hnoInternalFns, hSupported.noAdtTypes] at hcore\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":2291,"n_subproofs":8,"n_tactics":42,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_deploy_compileConstructor","depth":1,"n_commands":0,"n_lines":33,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hSupported.normalizedFields,\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\n hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · simp [hmap] at hcore\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\n rcases hctor :\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\n · simp [hctor] at hcore\n cases hcore\n · simp [hctor] at hcore\n cases hcore\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor","n_chars":1536,"n_subproofs":3,"n_tactics":33,"cyclomatic":5,"n_automation":8,"n_rewrites":2,"n_structural":4,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noFallbackEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10},{"theorem_name":"compileValidatedCore_ok_yields_noReceiveEntrypoint","depth":1,"n_commands":0,"n_lines":31,"is_leaf":true,"centrality":0,"method":"deleted-dep","proof_text":" by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl","n_chars":1689,"n_subproofs":3,"n_tactics":31,"cyclomatic":4,"n_automation":6,"n_rewrites":2,"n_structural":3,"automation_only":false,"max_nesting":10}],"string":"[\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_compiled_functions\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 47,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n have hfunctions : ir.functions = irFns := by\\n injection hcore with hir\\n cases hir\\n rfl\\n have hcompiled :\\n List.Forall₂\\n (fun (entry : FunctionSpec × Nat) irFn =>\\n compileFunctionSpec model.fields model.events model.errors [] entry.2 entry.1 = Except.ok irFn)\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors)\\n irFns :=\\n by\\n simpa [hSupported.noEvents, hSupported.noErrors] using\\n (compiled_functions_forall₂_of_mapM_ok model.fields [] [] _ _ hmap)\\n simpa [SourceSemantics.selectorFunctionPairs, selectorDispatchedFunctions,\\n hfunctions] using hcompiled\",\n \"n_chars\": 2206,\n \"n_subproofs\": 5,\n \"n_tactics\": 47,\n \"cyclomatic\": 5,\n \"n_automation\": 10,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 16\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_internalFunctions_nil\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 42,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n have harray : contractUsesArrayElement model = false :=\\n hSupported.contractUsesArrayElement_eq_false\\n have hstorageArray : contractUsesStorageArrayElement model = false :=\\n hSupported.contractUsesStorageArrayElement_eq_false\\n have hdynamicBytesEq : contractUsesDynamicBytesEq model = false :=\\n hSupported.contractUsesDynamicBytesEq_eq_false\\n have hmulDiv512 : contractUsesMulDiv512 model = false :=\\n hSupported.contractUsesMulDiv512_eq_false\\n have hparamDyn : contractUsesParamDynamicHeadWord model = false :=\\n hSupported.contractUsesParamDynamicHeadWord_eq_false\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields, hfallback, hreceive,\\n contractUsesPlainArrayElement, contractUsesArrayElementWord, harray,\\n hstorageArray, hdynamicBytesEq, hmulDiv512, hparamDyn,\\n hSupported.noCheckedArithmetic,\\n hnoInternalFns, hSupported.noAdtTypes] at hcore\\n simp only [bind, Except.bind, pure, Except.pure, List.mapM_nil] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields model.events model.errors [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields model.events model.errors [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor model.fields model.events model.errors [] model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 2291,\n \"n_subproofs\": 8,\n \"n_tactics\": 42,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_deploy_compileConstructor\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 33,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hSupported.normalizedFields,\\n hSupported.noAdtTypes, hSupported.noEvents, hSupported.noErrors,\\n hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq model.fields [] [] [] [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec model.fields [] [] [] x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · simp [hmap] at hcore\\n simp [hSupported.surface.noTemplateIntrinsics] at hcore\\n rcases hctor :\\n compileConstructor model.fields [] [] [] model.constructor with _ | deployStmts\\n · simp [hctor] at hcore\\n cases hcore\\n · simp [hctor] at hcore\\n cases hcore\\n simpa [hSupported.noEvents, hSupported.noErrors] using hctor\",\n \"n_chars\": 1536,\n \"n_subproofs\": 3,\n \"n_tactics\": 33,\n \"cyclomatic\": 5,\n \"n_automation\": 8,\n \"n_rewrites\": 2,\n \"n_structural\": 4,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noFallbackEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n },\n {\n \"theorem_name\": \"compileValidatedCore_ok_yields_noReceiveEntrypoint\",\n \"depth\": 1,\n \"n_commands\": 0,\n \"n_lines\": 31,\n \"is_leaf\": true,\n \"centrality\": 0,\n \"method\": \"deleted-dep\",\n \"proof_text\": \" by\\n have hfallback :\\n pickUniqueFunctionByName \\\"fallback\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"fallback\\\" model.functions hSupported.noFallback\\n have hreceive :\\n pickUniqueFunctionByName \\\"receive\\\" model.functions = Except.ok none :=\\n pickUniqueFunctionByName_eq_ok_none_of_absent\\n \\\"receive\\\" model.functions hSupported.noReceive\\n have hnoInternalFns :\\n model.functions.filter (·.isInternal) = [] :=\\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\\n unfold compileValidatedCore at hcore\\n rw [hnoInternalFns, hfallback, hreceive] at hcore\\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes [] _\\n (supportedSpec_entries_lock_free hSupported)] at hcore\\n rcases hmap :\\n ((model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\\n · simp [hmap] at hcore\\n · rcases hctor :\\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\\n cases hcore\\n rfl\",\n \"n_chars\": 1689,\n \"n_subproofs\": 3,\n \"n_tactics\": 31,\n \"cyclomatic\": 4,\n \"n_automation\": 6,\n \"n_rewrites\": 2,\n \"n_structural\": 3,\n \"automation_only\": false,\n \"max_nesting\": 10\n }\n]","isConversational":false},"deleted_lemmas":{"kind":"list like","value":[{"name":"supportedSpec_entries_lock_free","text":"theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\n","fan_in":5,"n_lines":11,"n_chars":464,"n_subproofs":1,"n_tactics":4,"cyclomatic":1,"n_automation":0,"n_rewrites":0,"n_structural":2,"automation_only":false,"max_nesting":2}],"string":"[\n {\n \"name\": \"supportedSpec_entries_lock_free\",\n \"text\": \"theorem supportedSpec_entries_lock_free\\n {model : CompilationModel} {selectors : List Nat}\\n (hSupported : SupportedSpec model selectors) :\\n ∀ e ∈ (model.functions.filter\\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\\n intro e he\\n have hmem := (List.of_mem_zip he).1\\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\\n\\n\",\n \"fan_in\": 5,\n \"n_lines\": 11,\n \"n_chars\": 464,\n \"n_subproofs\": 1,\n \"n_tactics\": 4,\n \"cyclomatic\": 1,\n \"n_automation\": 0,\n \"n_rewrites\": 0,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 2\n }\n]","isConversational":false},"corollaries":{"kind":"list like","value":[{"name":"compile_ok_yields_noFallbackEntrypoint","fan_in":0,"n_deps_direct":1,"n_deps_transitive":4,"n_lines":20,"n_chars":719,"n_subproofs":0,"n_tactics":12,"cyclomatic":2,"n_automation":3,"n_rewrites":1,"n_structural":2,"automation_only":false,"max_nesting":6}],"string":"[\n {\n \"name\": \"compile_ok_yields_noFallbackEntrypoint\",\n \"fan_in\": 0,\n \"n_deps_direct\": 1,\n \"n_deps_transitive\": 4,\n \"n_lines\": 20,\n \"n_chars\": 719,\n \"n_subproofs\": 0,\n \"n_tactics\": 12,\n \"cyclomatic\": 2,\n \"n_automation\": 3,\n \"n_rewrites\": 1,\n \"n_structural\": 2,\n \"automation_only\": false,\n \"max_nesting\": 6\n }\n]","isConversational":false},"closure_size":{"kind":"number","value":4,"string":"4"},"challenge_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_noFallbackEntrypoint\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.fallbackEntrypoint = none := sorry\n\ntheorem compile_ok_yields_noFallbackEntrypoint\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n ir.fallbackEntrypoint = none := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_noFallbackEntrypoint\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_file_content":{"kind":"string","value":"import Compiler.Proofs.IRGeneration.SourceSemantics\n\nset_option linter.unnecessarySimpa false\n\nnamespace Compiler.Proofs.IRGeneration\n\nopen Compiler\nopen Compiler.CompilationModel\n\nnamespace ContractShape\n\nprivate theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction funcs with\n | nil =>\n rfl\n | cons fn rest ih =>\n have hfn : (fn.name == name) = false := by\n by_cases heq : fn.name = name\n · have habs := habsent fn (by simp)\n simp [heq] at habs\n · simp [heq]\n have hrest : ∀ fn' ∈ rest, fn'.name != name := by\n intro fn' hmem\n exact habsent fn' (by simp [hmem])\n have ih' := ih hrest\n simpa [pickUniqueFunctionByName, hfn] using ih'\n\n/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentrantGuard_eq_of_none\n (fields : List Field) (spec : FunctionSpec) (irFn : IRFunction)\n (hnone : spec.nonReentrantLock = none) :\n attachNonReentrantGuard fields spec irFn = Except.ok irFn := by\n simp [attachNonReentrantGuard, hnone, pure, Except.pure]\n\ntheorem compileGuardedFunctionSpec_eq_of_none\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec)\n (sel : Nat) (fnSpec : FunctionSpec)\n (hnone : fnSpec.nonReentrantLock = none) :\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions sel fnSpec =\n compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions := by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes sel fnSpec\n (targetFork := .cancun) internalFunctions with\n | error err => simp [bind, Except.bind]\n | ok irFn =>\n simp [bind, Except.bind,\n attachNonReentrantGuard_eq_of_none fields fnSpec irFn hnone]\n\ntheorem guardedFunctionsMapM_eq\n (fields : List Field) (events : List EventDef) (errors : List ErrorDef)\n (adtTypes : List AdtTypeDef) (internalFunctions : List FunctionSpec) :\n ∀ (entries : List (FunctionSpec × Nat)),\n (∀ e ∈ entries, e.1.nonReentrantLock = none) →\n (entries.mapM fun entry =>\n compileGuardedFunctionSpec fields events errors adtTypes internalFunctions entry.2 entry.1) =\n entries.mapM fun entry =>\n compileFunctionSpec fields events errors adtTypes entry.2 entry.1\n (targetFork := .cancun) internalFunctions\n | [], _ => rfl\n | e :: rest, hnolock => by\n have hhead : e.1.nonReentrantLock = none := hnolock e (by simp)\n have htail := guardedFunctionsMapM_eq fields events errors adtTypes internalFunctions rest\n (fun e' he' => hnolock e' (List.mem_cons_of_mem _ he'))\n simp only [List.mapM_cons,\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n\ntheorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n intro e he\n have hmem := (List.of_mem_zip he).1\n exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n\nprivate theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n fns.filter (·.isInternal) = []\n | [], _ => rfl\n | fn :: rest, hall => by\n have hfn : fn.isInternal = false := hall fn (by simp)\n have hrest : ∀ fn' ∈ rest, fn'.isInternal = false := by\n intro fn' hmem\n exact hall fn' (by simp [hmem])\n simp [hfn, filterInternalFunctions_eq_nil_of_all_nonInternal rest hrest]\n\nprivate theorem filterInternalFunctions_eq_nil_of_supported\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors) :\n model.functions.filter (·.isInternal) = [] := by\n exact filterInternalFunctions_eq_nil_of_all_nonInternal model.functions\n (hSupported.noInternalFunctions)\n\nprivate theorem compileValidatedCore_ok_yields_noFallbackEntrypoint\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n ir.fallbackEntrypoint = none := by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"fallback\" model.functions hSupported.noFallback\n have hreceive :\n pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n pickUniqueFunctionByName_eq_ok_none_of_absent\n \"receive\" model.functions hSupported.noReceive\n have hnoInternalFns :\n model.functions.filter (·.isInternal) = [] :=\n filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n unfold compileValidatedCore at hcore\n rw [hnoInternalFns, hfallback, hreceive] at hcore\n simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes [] _\n (supportedSpec_entries_lock_free hSupported)] at hcore\n rcases hmap :\n ((model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n · simp [hmap] at hcore\n · rcases hctor :\n compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n cases hcore\n rfl\n\ntheorem compile_ok_yields_noFallbackEntrypoint\n (model : CompilationModel)\n (selectors : List Nat)\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcompile : CompilationModel.compile model selectors = Except.ok ir) :\n ir.fallbackEntrypoint = none := by\n unfold CompilationModel.compile at hcompile\n simp only [bind, Except.bind] at hcompile\n rcases hvalidate : validateCompileInputs model selectors with _ | validated\n · simp [hvalidate] at hcompile\n · simp [hvalidate] at hcompile\n exact compileValidatedCore_ok_yields_noFallbackEntrypoint\n (model := model)\n (selectors := selectors)\n (hSupported := hSupported)\n (ir := ir)\n (hcore := hcompile)\n\nend ContractShape\n\nend Compiler.Proofs.IRGeneration\n"},"solution_diff":{"kind":"string","value":"@@ -72,6 +72,16 @@\n compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,\n htail]\n \n+theorem supportedSpec_entries_lock_free\n+ {model : CompilationModel} {selectors : List Nat}\n+ (hSupported : SupportedSpec model selectors) :\n+ ∀ e ∈ (model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors,\n+ (e : FunctionSpec × Nat).1.nonReentrantLock = none := by\n+ intro e he\n+ have hmem := (List.of_mem_zip he).1\n+ exact (hSupported.functions e.1 (List.mem_filter.mp hmem).1).noNonReentrant\n+\n private theorem filterInternalFunctions_eq_nil_of_all_nonInternal :\n ∀ (fns : List FunctionSpec),\n (∀ fn ∈ fns, fn.isInternal = false) →\n@@ -98,7 +108,37 @@\n (hSupported : SupportedSpec model selectors)\n (ir : IRContract)\n (hcore : compileValidatedCore model selectors = Except.ok ir) :\n- ir.fallbackEntrypoint = none := sorry\n+ ir.fallbackEntrypoint = none := by\n+ have hfallback :\n+ pickUniqueFunctionByName \"fallback\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"fallback\" model.functions hSupported.noFallback\n+ have hreceive :\n+ pickUniqueFunctionByName \"receive\" model.functions = Except.ok none :=\n+ pickUniqueFunctionByName_eq_ok_none_of_absent\n+ \"receive\" model.functions hSupported.noReceive\n+ have hnoInternalFns :\n+ model.functions.filter (·.isInternal) = [] :=\n+ filterInternalFunctions_eq_nil_of_supported model selectors hSupported\n+ unfold compileValidatedCore at hcore\n+ rw [hnoInternalFns, hfallback, hreceive] at hcore\n+ simp only [bind, Except.bind, Option.mapM_none, pure, Except.pure] at hcore\n+ simp only [guardedFunctionsMapM_eq (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes [] _\n+ (supportedSpec_entries_lock_free hSupported)] at hcore\n+ rcases hmap :\n+ ((model.functions.filter\n+ (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name)).zip selectors).mapM\n+ (fun x => compileFunctionSpec (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes x.2 x.1) with _ | irFns\n+ · simp [hmap] at hcore\n+ · rcases hctor :\n+ compileConstructor (applySlotAliasRanges model.fields model.slotAliasRanges)\n+ model.events model.errors model.adtTypes model.constructor with _ | deployStmts\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n+ · simp [hmap, hctor, hSupported.surface.noTemplateIntrinsics, Pure.pure, Except.pure] at hcore\n+ cases hcore\n+ rfl\n \n theorem compile_ok_yields_noFallbackEntrypoint\n (model : CompilationModel)\n"},"manifest":{"kind":"string","value":"{\n \"repo\": \"verity\",\n \"git_repo\": \"github.com/lfglabs-dev/verity\",\n \"revision\": \"eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978\",\n \"lean_toolchain\": \"leanprover/lean4:v4.22.0\",\n \"proof_assistant\": \"lean\",\n \"ablator\": \"ablators/lean (corollary-delete-lemmas-leaves-all)\",\n \"ablator_flags\": [\n \"--corollary-delete-lemmas-leaves-all\",\n \"--shrink-solution-minimal\",\n \"--compact\",\n \"--seed\",\n \"42\"\n ],\n \"seed\": 42,\n \"validation\": \"ablate-baseline --dry-run (preflight compile of challenge + solution)\",\n \"counts\": {\n \"mined_total\": 1766,\n \"good_kept\": 1262,\n \"well_formed\": 1262,\n \"malformed\": 462,\n \"sol_bad\": 42\n }\n}"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":213,"numItemsPerPage":100,"numTotalItems":21692,"offset":21300,"length":100}},"jwt":"eyJhbGciOiJFZERTQSIsImtpZCI6IjVHZDBvd0g5MTM2eDZjc1FvbE1zcktNWUZoRVFoUm5PVVVybEpjOUhaUEEifQ.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc4NjU0Mjg2NiwianRpIjoiNzUxYmI5ZTMtNjA3My00YjI0LTk1MjYtNmIzMDkxMzBiMTE0Iiwic3ViIjoiL2RhdGFzZXRzL2Zvci1hbGwtZGV2L2FibGF0aW9uLWV2YWwiLCJleHAiOjE3ODY1NDY0NjYsImlzcyI6Imh0dHBzOi8vaHVnZ2luZ2ZhY2UuY28ifQ.Q8-eKi1rSkizhywOg3Z1y9jOL7xn7krYsbQ_tx1U0WHU9cZnBoPfMddKmPX8Hd_HFwRbUr_TDLHPAQT0EpzyDQ","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"easy","numRows":21692,"numBytesParquet":263721168},{"config":"default","split":"hard","numRows":21718,"numBytesParquet":263203815}]},"discussionsStats":{"closed":0,"open":1,"total":1},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">
task_id stringlengths 21 23 | challenge_id stringlengths 16 16 | proof_assistant stringclasses 1
value | session stringclasses 1
value | repo stringclasses 57
values | revision stringclasses 57
values | file_path stringlengths 13 92 | theory stringlengths 1 48 | variant int64 0 132 | challenge_type stringclasses 1
value | difficulty null | count null | by_centrality bool 1
class | ablation_prob float64 0.5 0.5 | min_depth int64 1 1 | max_depth int64 1 1 | leaves_only bool 1
class | min_size int64 0 0 | max_size stringclasses 1
value | min_centrality int64 0 0 | max_centrality stringclasses 1
value | seed int64 42 42 | n_proofs int64 1 173 | n_ablated int64 1 60 | holes_filled listlengths 1 60 | deleted_lemmas listlengths 1 1 | corollaries listlengths 1 1 | closure_size int64 1 172 | challenge_file_content stringlengths 133 350k | solution_file_content stringlengths 394 351k | solution_diff stringlengths 243 134k | manifest dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ablate_848d26072a8c_24 | 71eef49b85ddbc79 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "runtimeStateMatchesIR_writeUintKeyedMappingSlot",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 15,
"n_lines": 40,
"n_chars": 2206,
"n_subproofs": 0,
"n_tactics": 22,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 5,
"autom... | 12 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -310,6 +310,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_25 | c8e0aa9a9bb12073 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 25 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "runtimeStateMatchesIR_writeAddressKeyedMappingChainSlot",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 15,
"n_lines": 52,
"n_chars": 2561,
"n_subproofs": 1,
"n_tactics": 27,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 5,
"n_structural": 5,
... | 12 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -324,6 +324,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_26 | e299fb682fb5484e | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 26 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "runtimeStateMatchesIR_writeAddressKeyedMappingSlot",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 15,
"n_lines": 52,
"n_chars": 3081,
"n_subproofs": 1,
"n_tactics": 32,
"cyclomatic": 2,
"n_automation": 8,
"n_rewrites": 3,
"n_structural": 7,
"au... | 12 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -310,6 +310,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_27 | 404d679dc9377824 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 27 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "runtimeStateMatchesIR_writeAddressKeyedMappingWordSlot",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 16,
"n_lines": 53,
"n_chars": 2787,
"n_subproofs": 1,
"n_tactics": 30,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 5,
"n_structural": 5,
... | 12 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -339,6 +339,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_28 | 76de8457a18c2103 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 28 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "runtimeStateMatchesIR_writeAddressKeyedMapping2Slot",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 15,
"n_lines": 56,
"n_chars": 2689,
"n_subproofs": 0,
"n_tactics": 28,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 3,
"n_structural": 5,
"a... | 12 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -310,6 +310,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_29 | beb7a4e2cf766269 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 29 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 16,
"n_lines": 54,
"n_chars": 2893,
"n_subproofs": 1,
"n_tactics": 31,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 5,
"n_structural": 5,
... | 13 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -313,6 +313,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_30 | fe59b64b48c5ccdd | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 30 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 2 | [
{
"theorem_name": "runtimeStateMatchesIR_writeUintSlots",
"depth": 1,
"n_commands": 0,
"n_lines": 41,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchai... | [
{
"name": "abstractStoreStorageOrMappingMany_eq",
"text": "private theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRS... | [
{
"name": "bindingsExactlyMatchIRVarsOnScope_writeUintSlots",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 562,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automat... | 1 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -770,6 +770,26 @@
rest
value
+private theorem abstractStoreStorageOrMappingMany_eq
+ {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →
+ Compiler.Proofs.IRGeneration.IRStorageWord}
+ {slots : List Nat}
+ {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :
+ ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_31 | c6867784ea6da238 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 31 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "execIRStmts_let_then_sstore_lit_ident_slots_continue",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hlet :\n execIRStmt (slots.length + fuel + 1) state\n (YulStmt.let_ ... | [
{
"name": "execIRStmts_sstore_lit_ident_slots_continue",
"text": "private theorem execIRStmts_sstore_lit_ident_slots_continue\n (fuel : Nat)\n (state : IRState)\n (slots : List Nat)\n (name : String)\n (value : Nat)\n (hvalue : IRState.getVar state name = value) :\n execIRStmts (slots.l... | [
{
"name": "execIRStmts_let_then_sstore_lit_ident_slots_continue",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 35,
"n_chars": 1138,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"a... | 1 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -842,6 +842,42 @@
(by simpa [htgt, mappingWordTargetSlot] using
IRStorageSlot.ne_toNat_wordNormalize_of_ne_ofNat hEq)).symm
+private theorem execIRStmts_sstore_lit_ident_slots_continue
+ (fuel : Nat)
+ (state : IRState)
+ (slots : List Nat)
+ (name : String)
+ (value : Nat)
+... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_32 | 81aff33f18cea657 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 32 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "validateIdentifierShapes_fieldName_ne_reservedScratch",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n Comp... | [
{
"name": "compatScratch_not_internalImmutable",
"text": "private theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.star... | [
{
"name": "validateIdentifierShapes_fieldName_ne_reservedScratch",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 43,
"n_chars": 2071,
"n_subproofs": 9,
"n_tactics": 33,
"cyclomatic": 2,
"n_automation": 13,
"n_rewrites": 0,
"n_structural": 18,
... | 2 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -966,6 +966,122 @@
left
decide
+private theorem compatScratch_not_internalImmutable
+ {name : String}
+ (h :
+ name = "__compat_value" ∨
+ name = "__compat_packed" ∨
+ name = "__compat_slot_word" ∨
+ name = "__compat_slot_cleared") :
+ name.startsWith "__immut... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_33 | edd278060f3514cd | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 33 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "validateIdentifierShapes_fieldName_ne_reservedScratch",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases List.mem_map.mp hmem with ⟨field, hfield, rfl⟩\n have hreserved :=\n Comp... | [
{
"name": "compatScratch_not_internalImmutable",
"text": "private theorem compatScratch_not_internalImmutable\n {name : String}\n (h :\n name = \"__compat_value\" ∨\n name = \"__compat_packed\" ∨\n name = \"__compat_slot_word\" ∨\n name = \"__compat_slot_cleared\") :\n name.star... | [
{
"name": "scopeAvoidsReservedCompilerPrefix_of_validateIdentifierShapes",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 101,
"n_chars": 5472,
"n_subproofs": 8,
"n_tactics": 86,
"cyclomatic": 13,
"n_automation": 20,
"n_rewrites": 0,
"n_structural... | 3 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -966,6 +966,122 @@
left
decide
+private theorem compatScratch_not_internalImmutable
+ {name : String}
+ (h :
+ name = "__compat_value" ∨
+ name = "__compat_packed" ∨
+ name = "__compat_slot_word" ∨
+ name = "__compat_slot_cleared") :
+ name.startsWith "__immut... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_34 | 604891ee06ff228a | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 34 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member",
"depth": 1,
"n_commands": 0,
"n_lines": 45,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithRe... | [
{
"name": "fieldWriteEntriesAt_packed_none_of_unpacked",
"text": "private theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry... | [
{
"name": "compiledStmtStep_setStorage_singleSlot",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 27,
"n_lines": 89,
"n_chars": 4699,
"n_subproofs": 12,
"n_tactics": 64,
"cyclomatic": 3,
"n_automation": 11,
"n_rewrites": 2,
"n_structural": 7,
"automation_o... | 22 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -363,6 +363,18 @@
SourceSemantics.wordNormalize]
exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩
+private theorem fieldWriteEntriesAt_packed_none_of_unpacked
+ {idx : Nat} {field : Field} {packed : Option PackedBits}
+ (hunpacked : field.packedBits = none)
+ (hmem : packed ∈ (fieldWri... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_35 | a87fa712be878f63 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 35 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member",
"depth": 1,
"n_commands": 0,
"n_lines": 45,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithRe... | [
{
"name": "fieldWriteEntriesAt_packed_none_of_unpacked",
"text": "private theorem fieldWriteEntriesAt_packed_none_of_unpacked\n {idx : Nat} {field : Field} {packed : Option PackedBits}\n (hunpacked : field.packedBits = none)\n (hmem : packed ∈ (fieldWriteEntriesAt idx field).map (fun entry => entry... | [
{
"name": "compiledStmtStep_setStorageAddr_singleSlot_preserves",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 26,
"n_lines": 140,
"n_chars": 6721,
"n_subproofs": 14,
"n_tactics": 92,
"cyclomatic": 3,
"n_automation": 16,
"n_rewrites": 2,
"n_structural": 8,
... | 21 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -347,6 +347,18 @@
SourceSemantics.wordNormalize]
exact Or.inr ⟨_, _, _, _, halias, rfl, rfl, rfl⟩
+private theorem fieldWriteEntriesAt_packed_none_of_unpacked
+ {idx : Nat} {field : Field} {packed : Option PackedBits}
+ (hunpacked : field.packedBits = none)
+ (hmem : packed ∈ (fieldWri... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_36 | 8d273e09d4a7ef58 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 36 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked",
"depth": 1,
"n_commands": 0,
"n_lines": 35,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | c... | [
{
"name": "list_findSlotPackedNone_ne_none",
"text": "private theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2... | [
{
"name": "compiledStmtStep_setStorageAddr_singleSlot",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 27,
"n_lines": 28,
"n_chars": 1334,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_... | 22 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -381,13 +381,73 @@
| some conflict => some conflict
| none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest
+private theorem list_findSlotPackedNone_ne_none
+ {seen : List (Nat × String × Option PackedBits)}
+ {slot : Nat}
+ (hmem : slot ∈ seen.map (fun entr... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_39 | ed6f3ddd7ac0834a | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 39 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 18,
"n_lines": 192,
"n_chars": 10615,
"n_subproofs": 21,
"n_tactics": 141,
"cyclomatic": 7,
"n_automation": 23,
"n_rewrites": 3,
"n_st... | 15 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -310,6 +310,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_40 | c33c4b85b9fb171b | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 40 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setMappingUint_singleSlot_of_slotSafety",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 21,
"n_lines": 39,
"n_chars": 2096,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
... | 18 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -316,6 +316,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_41 | c186e7d89ee9be7c | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 41 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 14 | [
{
"theorem_name": "compiledStmtStep_mstore_single",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\n have hvalueIRInternal := compileE... | [
{
"name": "compileExprWithInternals_nil_ok",
"text": "private theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.c... | [
{
"name": "compileExprList_core_ok",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 25,
"n_chars": 1179,
"n_subproofs": 4,
"n_tactics": 19,
"cyclomatic": 4,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"... | 2 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -12,6 +12,12 @@
attribute [local simp] CompilationModel.compileExprWithInternals_nil_eq
+private theorem compileExprWithInternals_nil_ok
+ {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}
+ (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok ex... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_42 | e2d300fc533028af | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 42 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 14 | [
{
"theorem_name": "compiledStmtStep_mstore_single",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\n have hvalueIRInternal := compileE... | [
{
"name": "compileExprWithInternals_nil_ok",
"text": "private theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.c... | [
{
"name": "compileStmt_emit_scalar_supported_ok",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 43,
"n_chars": 2096,
"n_subproofs": 7,
"n_tactics": 32,
"cyclomatic": 5,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 7,
"automation_only":... | 3 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -12,6 +12,12 @@
attribute [local simp] CompilationModel.compileExprWithInternals_nil_eq
+private theorem compileExprWithInternals_nil_ok
+ {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}
+ (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok ex... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_43 | 966b0fafd47164a0 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 43 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 4 | [
{
"theorem_name": "compileExprList_core_ok",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction exprs with\n | nil =>\n exact ⟨[], by\n simp [CompilationModel.compileExprList, Compilation... | [
{
"name": "compileExprListWithInternals_nil_ok",
"text": "private theorem compileExprListWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {exprs : List Expr}\n {exprIRs : List YulExpr}\n (h : CompilationModel.compileExprList fields dynamicSource exprs = Except.ok exp... | [
{
"name": "eventHeadStepBridgeCatalog_of_semanticBridgeCatalog",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 45,
"n_chars": 1288,
"n_subproofs": 0,
"n_tactics": 35,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 5,
"au... | 4 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -18,6 +18,14 @@
CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by
simpa [CompilationModel.compileExprWithInternals_nil_eq] using h
+private theorem compileExprListWithInternals_nil_ok
+ {fields : List Field} {dynamicSource : DynamicDataSource} {exprs : List ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_44 | dce41d71dcff6866 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 44 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 4 | [
{
"theorem_name": "compileExprList_core_ok",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction exprs with\n | nil =>\n exact ⟨[], by\n simp [CompilationModel.compileExprList, Compilation... | [
{
"name": "compileExprListWithInternals_nil_ok",
"text": "private theorem compileExprListWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {exprs : List Expr}\n {exprIRs : List YulExpr}\n (h : CompilationModel.compileExprList fields dynamicSource exprs = Except.ok exp... | [
{
"name": "eval_compileExprList_core_of_scope",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 51,
"n_chars": 2635,
"n_subproofs": 5,
"n_tactics": 33,
"cyclomatic": 7,
"n_automation": 8,
"n_rewrites": 1,
"n_structural": 13,
"automation_only": ... | 4 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -18,6 +18,14 @@
CompilationModel.compileExprWithInternals fields dynamicSource [] expr = Except.ok exprIR := by
simpa [CompilationModel.compileExprWithInternals_nil_eq] using h
+private theorem compileExprListWithInternals_nil_ok
+ {fields : List Field} {dynamicSource : DynamicDataSource} {exprs : List ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_45 | f51a8d94319bac9f | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 45 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "evalIRExpr_mapping2WordTarget_of_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hMappingSlot2Eval :\n evalIRExpr state\n (YulExpr.call \"mappingSlot\"\n [... | [
{
"name": "evalIRExpr_mappingSlot2_of_eval",
"text": "private theorem evalIRExpr_mappingSlot2_of_eval\n {state : IRState} {slot key1Nat key2Nat : Nat}\n {key1IR key2IR : YulExpr}\n (hkey1 : evalIRExpr state key1IR = some key1Nat)\n (hkey2 : evalIRExpr state key2IR = some key2Nat) :\n evalIREx... | [
{
"name": "evalIRExpr_mapping2WordTarget_of_eval",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 37,
"n_chars": 1749,
"n_subproofs": 3,
"n_tactics": 25,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 0,
"automation_only"... | 3 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -996,6 +996,26 @@
else state.transientStorage slot } := by
simp [execIRStmt, hslot, hvalue]
+private theorem evalIRExpr_mappingSlot2_of_eval
+ {state : IRState} {slot key1Nat key2Nat : Nat}
+ {key1IR key2IR : YulExpr}
+ (hkey1 : evalIRExpr state key1IR = some key1Nat)
+ (hkey2 : evalIRE... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_46 | 3165f16d9764a685 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 46 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setMappingChain_singleSlot_of_slotSafety_preserves",
"fan_in": 1,
"n_deps_direct": 7,
"n_deps_transitive": 27,
"n_lines": 220,
"n_chars": 11533,
"n_subproofs": 24,
"n_tactics": 157,
"cyclomatic": 9,
"n_automation": 26,
"n_rewrites": 2,
"n_s... | 21 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -338,6 +338,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_47 | d216432b1843e835 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 47 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 6 | [
{
"theorem_name": "compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves",
"depth": 1,
"n_commands": 0,
"n_lines": 142,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n... | [
{
"name": "runtimeStateMatchesIR_writeTransientTarget",
"text": "private theorem runtimeStateMatchesIR_writeTransientTarget\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {target value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields run... | [
{
"name": "compiledStmtStep_setMappingChain_singleSlot_of_slotSafety",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 29,
"n_lines": 43,
"n_chars": 2278,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
... | 23 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -885,6 +885,40 @@
rest
value
+private theorem runtimeStateMatchesIR_writeTransientTarget
+ {fields : List Field}
+ {runtime : SourceSemantics.RuntimeState}
+ {state : IRState}
+ {target value : Nat}
+ (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)
+ (hvalue... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_48 | 556fa1637638b3a3 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 48 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setMapping_singleSlot_of_slotSafety_preserves",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 18,
"n_lines": 192,
"n_chars": 10589,
"n_subproofs": 21,
"n_tactics": 141,
"cyclomatic": 7,
"n_automation": 23,
"n_rewrites": 3,
"n_struct... | 15 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -310,6 +310,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_49 | 876efbfba3dc76fa | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 49 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setMapping_singleSlot_of_slotSafety",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 21,
"n_lines": 39,
"n_chars": 2084,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"... | 18 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -316,6 +316,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_50 | 0c8a25d2385c3add | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 50 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setMappingWord_singleSlot_of_slotSafety_preserves",
"fan_in": 2,
"n_deps_direct": 9,
"n_deps_transitive": 25,
"n_lines": 224,
"n_chars": 12626,
"n_subproofs": 22,
"n_tactics": 165,
"cyclomatic": 7,
"n_automation": 26,
"n_rewrites": 5,
"n_st... | 16 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -339,6 +339,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_51 | 8b161029ad4a4567 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 51 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "runtimeStateMatchesIR_writeAddressKeyedMappingWordSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimest... | [
{
"name": "encodeStorageAt_writeAddressKeyedMappingWordSlots_singleton_eq_written",
"text": "private theorem encodeStorageAt_writeAddressKeyedMappingWordSlots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key wordOffset value : Nat}\n (hresolved :\n f... | [
{
"name": "compiledStmtStep_setMappingWord_singleSlot_of_slotSafety",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 28,
"n_lines": 42,
"n_chars": 2263,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
... | 19 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -780,6 +780,56 @@
SourceSemantics.encodeStorageAt fields world slot = (world.storageAddr slot).val := by
simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, haddr]
+private theorem encodeStorageAt_writeAddressKeyedMappingWordSlots_singleton_eq_written
+ {fields : List Field}
+ {world : Ve... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_53 | b8234ee0df341672 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 53 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setStructMember_singleSlot_of_slotSafety_preserves",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 26,
"n_lines": 78,
"n_chars": 4172,
"n_subproofs": 1,
"n_tactics": 16,
"cyclomatic": 5,
"n_automation": 3,
"n_rewrites": 1,
"n_struct... | 17 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -339,6 +339,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_54 | a35f2a11e03a626f | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 54 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 6 | [
{
"theorem_name": "compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves",
"depth": 1,
"n_commands": 0,
"n_lines": 142,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n... | [
{
"name": "runtimeStateMatchesIR_writeTransientTarget",
"text": "private theorem runtimeStateMatchesIR_writeTransientTarget\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {target value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields run... | [
{
"name": "compiledStmtStep_setStructMember_singleSlot_of_slotSafety",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 29,
"n_lines": 50,
"n_chars": 2674,
"n_subproofs": 2,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
... | 20 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -898,6 +898,40 @@
rest
value
+private theorem runtimeStateMatchesIR_writeTransientTarget
+ {fields : List Field}
+ {runtime : SourceSemantics.RuntimeState}
+ {state : IRState}
+ {target value : Nat}
+ (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)
+ (hvalue... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_55 | 9e4fc1664b8307f5 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 55 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setMapping2_singleSlot_of_slotSafety_preserves",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 18,
"n_lines": 232,
"n_chars": 13180,
"n_subproofs": 23,
"n_tactics": 169,
"cyclomatic": 8,
"n_automation": 27,
"n_rewrites": 4,
"n_struc... | 15 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -310,6 +310,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_56 | f231c26a5ce32a1c | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 56 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "runtimeStateMatchesIR_writeAddressKeyedMapping2Slot",
"depth": 1,
"n_commands": 0,
"n_lines": 28,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp... | [
{
"name": "encodeStorageAt_writeAddressKeyedMapping2Slots_singleton_eq_written",
"text": "private theorem encodeStorageAt_writeAddressKeyedMapping2Slots_singleton_eq_written\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 value : Nat}\n (hresolved :\n findResolved... | [
{
"name": "compiledStmtStep_setMapping2_singleSlot_of_slotSafety",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 21,
"n_lines": 48,
"n_chars": 2726,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
... | 18 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -839,6 +839,62 @@
· simp [SourceSemantics.writeAddressKeyedMapping2Slots]
· simp [SourceSemantics.writeAddressKeyedMapping2Slots]
+private theorem encodeStorageAt_writeAddressKeyedMapping2Slots_singleton_eq_written
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot key1 key2 va... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_57 | bc434ae629a66d07 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 57 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 12 | [
{
"theorem_name": "encodeStorageAt_eq_storage_of_resolvedSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [encodeStorageAt_eq_copy, encodeStorageAtCopy, hresolved, hnotAddr, hnotDyn]",
"n_char... | [
{
"name": "encodeStorageAt_eq_copy",
"text": "private theorem encodeStorageAt_eq_copy\n {fields : List Field}\n {world : Verity.ContractState}\n {slot : Nat} :\n SourceSemantics.encodeStorageAt fields world slot =\n encodeStorageAtCopy fields world slot := by\n simp only [SourceSemantics.e... | [
{
"name": "compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety_preserves",
"fan_in": 2,
"n_deps_direct": 9,
"n_deps_transitive": 27,
"n_lines": 279,
"n_chars": 16151,
"n_subproofs": 26,
"n_tactics": 207,
"cyclomatic": 8,
"n_automation": 28,
"n_rewrites": 8,
"n_s... | 19 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -313,6 +313,17 @@
simp only [findDynamicArrayElementAtSlotCopy]
exact findDynamicArrayElementAtSlotCopy_go_wordNormalize fields world 0 targetSlot
+private theorem encodeStorageAt_eq_copy
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot : Nat} :
+ SourceSemantics.encodeStorageAt f... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_58 | 4cc45e00c5411e5d | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 58 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 6 | [
{
"theorem_name": "compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves",
"depth": 1,
"n_commands": 0,
"n_lines": 142,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n... | [
{
"name": "runtimeStateMatchesIR_writeTransientTarget",
"text": "private theorem runtimeStateMatchesIR_writeTransientTarget\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {target value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields run... | [
{
"name": "compiledStmtStep_setMapping2Word_singleSlot_of_slotSafety",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 30,
"n_lines": 49,
"n_chars": 2812,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
... | 22 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -925,6 +925,40 @@
rest
value
+private theorem runtimeStateMatchesIR_writeTransientTarget
+ {fields : List Field}
+ {runtime : SourceSemantics.RuntimeState}
+ {state : IRState}
+ {target value : Nat}
+ (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)
+ (hvalue... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_59 | 39e1e7e9f35c9887 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 59 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "runtimeStateMatchesIR_writeAddressKeyedMapping2WordSlot",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimes... | [
{
"name": "encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other",
"text": "private theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other\n {fields : List Field}\n {world : Verity.ContractState}\n {slot key1 key2 wordOffset query value : Nat}\n (hneq :\n qu... | [
{
"name": "compiledStmtStep_setStructMember2_singleSlot_of_slotSafety_preserves",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 28,
"n_lines": 85,
"n_chars": 4957,
"n_subproofs": 1,
"n_tactics": 19,
"cyclomatic": 7,
"n_automation": 3,
"n_rewrites": 1,
"n_struc... | 20 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -802,6 +802,55 @@
simpa [mappingWordTargetSlot, SourceSemantics.wordNormalize,
Compiler.Proofs.abstractMappingSlot_eq_solidity] using hlt
+private theorem encodeStorageAt_writeAddressKeyedMapping2WordSlots_singleton_other
+ {fields : List Field}
+ {world : Verity.ContractState}
+ {slot key1 key2 w... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_60 | 1f330491ac5d1a12 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 60 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 6 | [
{
"theorem_name": "compiledStmtStep_setMappingUint_singleSlot_of_slotSafety_preserves",
"depth": 1,
"n_commands": 0,
"n_lines": 142,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro runtime state extraFuel hexact hscope hbounded hruntime hslack\n... | [
{
"name": "runtimeStateMatchesIR_writeTransientTarget",
"text": "private theorem runtimeStateMatchesIR_writeTransientTarget\n {fields : List Field}\n {runtime : SourceSemantics.RuntimeState}\n {state : IRState}\n {target value : Nat}\n (hruntime : FunctionBody.runtimeStateMatchesIR fields run... | [
{
"name": "compiledStmtStep_setStructMember2_singleSlot_of_slotSafety",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 31,
"n_lines": 48,
"n_chars": 3076,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,... | 23 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -925,6 +925,40 @@
rest
value
+private theorem runtimeStateMatchesIR_writeTransientTarget
+ {fields : List Field}
+ {runtime : SourceSemantics.RuntimeState}
+ {state : IRState}
+ {target value : Nat}
+ (hruntime : FunctionBody.runtimeStateMatchesIR fields runtime state)
+ (hvalue... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_61 | 4188872ddfe8f059 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 61 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 2 | [
{
"theorem_name": "firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_singleton",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n exact\n firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n ... | [
{
"name": "firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member",
"text": "private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member\n {seen : List (Nat × String × Option PackedBits)}\n {fields : List Field}\n {idx : Nat}\n {fieldName : String}\n {f : Field}\n {s... | [
{
"name": "compiledStmtStep_setStorage_aliasSlots",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 30,
"n_lines": 178,
"n_chars": 8970,
"n_subproofs": 26,
"n_tactics": 142,
"cyclomatic": 5,
"n_automation": 22,
"n_rewrites": 4,
"n_structural": 13,
"automatio... | 25 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -467,6 +467,68 @@
exact (ih hseen' hrest' hunpackedRest) hnone
· rw [hfind] at hnone; simp at hnone
+private theorem firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member
+ {seen : List (Nat × String × Option PackedBits)}
+ {fields : List Field}
+ {idx : Nat}
+ {fieldName : S... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_62 | 5af480282371e01e | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 62 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 2 | [
{
"theorem_name": "findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_memb... | [
{
"name": "findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member",
"text": "theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hno... | [
{
"name": "compiledStmtStep_setStorage_of_validateIdentifierShapes",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 41,
"n_lines": 73,
"n_chars": 2940,
"n_subproofs": 0,
"n_tactics": 41,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 4,
... | 35 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -674,6 +674,32 @@
| some _ =>
simp [hc]
+theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member
+ {fields : List Field}
+ {fieldName : String}
+ {f : Field}
+ {slot : Nat}
+ {writeSlots : List Nat}
+ {targetSlot : Nat}
+ (hnoConflict : firstFieldWriteSlotConflict... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_63 | 92c9808cab04b41c | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 63 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 2 | [
{
"theorem_name": "findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_singleton",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n exact\n findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_memb... | [
{
"name": "findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member",
"text": "theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member\n {fields : List Field}\n {fieldName : String}\n {f : Field}\n {slot : Nat}\n {writeSlots : List Nat}\n {targetSlot : Nat}\n (hno... | [
{
"name": "compiledStmtStep_setStorage_of_validateIdentifierShapes_of_scopeDiscipline",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 42,
"n_lines": 88,
"n_chars": 3627,
"n_subproofs": 3,
"n_tactics": 52,
"cyclomatic": 6,
"n_automation": 5,
"n_rewrites": 2,
"n... | 36 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -674,6 +674,32 @@
| some _ =>
simp [hc]
+theorem findResolvedFieldAtSlotCopy_of_findFieldWithResolvedSlot_member
+ {fields : List Field}
+ {fieldName : String}
+ {f : Field}
+ {slot : Nat}
+ {writeSlots : List Nat}
+ {targetSlot : Nat}
+ (hnoConflict : firstFieldWriteSlotConflict... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_64 | 46fa4d73ae1b6246 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 64 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 2 | [
{
"theorem_name": "runtimeStateMatchesIR_writeUintSlots",
"depth": 1,
"n_commands": 0,
"n_lines": 41,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchai... | [
{
"name": "abstractStoreStorageOrMappingMany_eq",
"text": "private theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRS... | [
{
"name": "compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 43,
"n_lines": 59,
"n_chars": 2634,
"n_subproofs": 0,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 1,
"n... | 37 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -804,6 +804,26 @@
rest
value
+private theorem abstractStoreStorageOrMappingMany_eq
+ {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →
+ Compiler.Proofs.IRGeneration.IRStorageWord}
+ {slots : List Nat}
+ {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :
+ ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_65 | 9252f946aca1f4a6 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 65 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 2 | [
{
"theorem_name": "runtimeStateMatchesIR_writeUintSlots",
"depth": 1,
"n_commands": 0,
"n_lines": 41,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hruntime with\n ⟨hstorage, htransient, hsender, hmsgValue, hthis, htimestamp, hblock, hchai... | [
{
"name": "abstractStoreStorageOrMappingMany_eq",
"text": "private theorem abstractStoreStorageOrMappingMany_eq\n {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →\n Compiler.Proofs.IRGeneration.IRStorageWord}\n {slots : List Nat}\n {value : Nat} {query : Compiler.Proofs.IRGeneration.IRS... | [
{
"name": "compiledStmtStep_setStorage_of_validateIdentifierShapes_of_validateFunctionIdentifierReferences_of_compileStmtList_of_bodySurface",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 44,
"n_lines": 62,
"n_chars": 3566,
"n_subproofs": 6,
"n_tactics": 28,
"cyclomatic"... | 38 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -804,6 +804,26 @@
rest
value
+private theorem abstractStoreStorageOrMappingMany_eq
+ {storage : Compiler.Proofs.IRGeneration.IRStorageSlot →
+ Compiler.Proofs.IRGeneration.IRStorageWord}
+ {slots : List Nat}
+ {value : Nat} {query : Compiler.Proofs.IRGeneration.IRStorageSlot} :
+ ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_66 | 6ce611d588899001 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 66 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 14 | [
{
"theorem_name": "compiledStmtStep_mstore_single",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\n have hvalueIRInternal := compileE... | [
{
"name": "compileExprWithInternals_nil_ok",
"text": "private theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.c... | [
{
"name": "compiledStmtStep_ite",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 248,
"n_chars": 13312,
"n_subproofs": 32,
"n_tactics": 230,
"cyclomatic": 8,
"n_automation": 29,
"n_rewrites": 20,
"n_structural": 25,
"automation_only": false,
... | 2 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -12,6 +12,12 @@
attribute [local simp] CompilationModel.compileExprWithInternals_nil_eq
+private theorem compileExprWithInternals_nil_ok
+ {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}
+ (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok ex... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_67 | 91aebdb5b7e89c96 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 67 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction stmts with\n | nil => simp [stmtListTou... | [
{
"name": "stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface",
"text": "private theorem stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface\n {stmt : Stmt}\n (hsurface : stmtTouchesUnsupportedContractSurface stmt = false) :\n stmtT... | [
{
"name": "stmtListTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 661,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites"... | 1 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -1925,13 +1925,25 @@
simp [stmtStepMatchesIRExec]
exact ⟨hruntime', hexact', hbounded, hscope'⟩
+private theorem stmtTouchesUnsupportedContractSurfaceExceptMappingWrites_eq_false_of_contractSurface
+ {stmt : Stmt}
+ (hsurface : stmtTouchesUnsupportedContractSurface stmt = false) :
+ stmtTouc... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_68 | f24a4f10592d8415 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 68 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 2 | [
{
"theorem_name": "firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member",
"depth": 1,
"n_commands": 0,
"n_lines": 45,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithRe... | [
{
"name": "fieldWriteEntriesAt_alias_mem",
"text": "private theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtai... | [
{
"name": "compiledStmtStep_assignStorageField",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 24,
"n_lines": 69,
"n_chars": 4251,
"n_subproofs": 7,
"n_tactics": 64,
"cyclomatic": 5,
"n_automation": 18,
"n_rewrites": 8,
"n_structural": 9,
"automation_only"... | 18 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -309,6 +309,44 @@
· obtain ⟨i, hi⟩ := ih (start := start + 1) hmem
exact ⟨i, by simp [List.zipIdx, hi]⟩
+private theorem fieldWriteEntriesAt_alias_mem
+ {idx : Nat} {field : Field} {slot : Nat}
+ (hmem : slot ∈ field.aliasSlots) :
+ SourceSemantics.wordNormalize slot ∈
+ (fieldWriteEn... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_69 | 843895de6034f8f0 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 69 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 2 | [
{
"theorem_name": "firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member",
"depth": 1,
"n_commands": 0,
"n_lines": 45,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithRe... | [
{
"name": "fieldWriteEntriesAt_alias_mem",
"text": "private theorem fieldWriteEntriesAt_alias_mem\n {idx : Nat} {field : Field} {slot : Nat}\n (hmem : slot ∈ field.aliasSlots) :\n SourceSemantics.wordNormalize slot ∈\n (fieldWriteEntriesAt idx field).map (fun entry => entry.1) := by\n obtai... | [
{
"name": "stmtListGenericCore_singleton_assignStorageField",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 25,
"n_lines": 15,
"n_chars": 604,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automa... | 19 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -309,6 +309,44 @@
· obtain ⟨i, hi⟩ := ih (start := start + 1) hmem
exact ⟨i, by simp [List.zipIdx, hi]⟩
+private theorem fieldWriteEntriesAt_alias_mem
+ {idx : Nat} {field : Field} {slot : Nat}
+ (hmem : slot ∈ field.aliasSlots) :
+ SourceSemantics.wordNormalize slot ∈
+ (fieldWriteEn... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_70 | eedf2ed12d1c359c | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 70 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 14 | [
{
"theorem_name": "compiledStmtStep_mstore_single",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hoffsetIRInternal := compileExprWithInternals_nil_ok hoffsetIR\n have hvalueIRInternal := compileE... | [
{
"name": "compileExprWithInternals_nil_ok",
"text": "private theorem compileExprWithInternals_nil_ok\n {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}\n (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok exprIR) :\n CompilationModel.c... | [
{
"name": "stmtListGenericCore_singleton_iteTerminal",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 15,
"n_chars": 659,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_onl... | 3 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -12,6 +12,12 @@
attribute [local simp] CompilationModel.compileExprWithInternals_nil_eq
+private theorem compileExprWithInternals_nil_ok
+ {fields : List Field} {dynamicSource : DynamicDataSource} {expr : Expr} {exprIR : YulExpr}
+ (h : CompilationModel.compileExpr fields dynamicSource expr = Except.ok ex... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_71 | cc93062013058d97 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 71 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked",
"depth": 1,
"n_commands": 0,
"n_lines": 35,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | c... | [
{
"name": "list_findSlotPackedNone_ne_none",
"text": "private theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2... | [
{
"name": "stmtListGenericCore_singleton_setStorage_singleSlot",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 29,
"n_lines": 34,
"n_chars": 1288,
"n_subproofs": 0,
"n_tactics": 21,
"cyclomatic": 3,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 4,
"a... | 23 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -397,13 +397,73 @@
| some conflict => some conflict
| none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest
+private theorem list_findSlotPackedNone_ne_none
+ {seen : List (Nat × String × Option PackedBits)}
+ {slot : Nat}
+ (hmem : slot ∈ seen.map (fun entr... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_72 | 540728b25bf44833 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 72 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked",
"depth": 1,
"n_commands": 0,
"n_lines": 35,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction current generalizing seen with\n | nil =>\n simp at hcurrent\n | c... | [
{
"name": "list_findSlotPackedNone_ne_none",
"text": "private theorem list_findSlotPackedNone_ne_none\n {seen : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hmem : slot ∈ seen.map (fun entry => entry.1)) :\n (seen.find? (fun entry => entry.1 == slot && packedSlotsConflict entry.2.2... | [
{
"name": "stmtListGenericCore_singleton_setStorageAddr_singleSlot",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 29,
"n_lines": 25,
"n_chars": 1011,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
... | 23 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -381,13 +381,73 @@
| some conflict => some conflict
| none => firstFieldWriteSlotConflictCopyFrom (writeSlots.reverse ++ seen) (idx + 1) rest
+private theorem list_findSlotPackedNone_ne_none
+ {seen : List (Nat × String × Option PackedBits)}
+ {slot : Nat}
+ (hmem : slot ∈ seen.map (fun entr... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_75 | e8da6ae65a447190 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 75 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member",
"depth": 1,
"n_commands": 0,
"n_lines": 45,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithRe... | [
{
"name": "firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked",
"text": "private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ cu... | [
{
"name": "stmtListGenericCore_of_supportedStmtList_setStorageSingleSlot_of_surface",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 30,
"n_lines": 21,
"n_chars": 771,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_str... | 24 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -423,6 +423,48 @@
· simp
· exact hih
+private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked
+ {seen current : List (Nat × String × Option PackedBits)}
+ {slot : Nat}
+ (hseen : slot ∈ seen.map (fun entry => entry.1))
+ (hcurrent : slot ∈ current.map (fun entry => entr... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_848d26072a8c_76 | da08cf166bb4d54a | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Storage.lean | Storage | 76 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 97 | 1 | [
{
"theorem_name": "firstFieldWriteSlotConflictCopyFrom_some_of_seen_slot_member",
"depth": 1,
"n_commands": 0,
"n_lines": 45,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction fields generalizing seen idx with\n | nil => simp [findFieldWithRe... | [
{
"name": "firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked",
"text": "private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked\n {seen current : List (Nat × String × Option PackedBits)}\n {slot : Nat}\n (hseen : slot ∈ seen.map (fun entry => entry.1))\n (hcurrent : slot ∈ cu... | [
{
"name": "stmtListGenericCore_of_supportedStmtList_setStorageAddrSingleSlot_of_surface",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 30,
"n_lines": 21,
"n_chars": 783,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n... | 24 | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | import Compiler.Proofs.IRGeneration.GenericInduction.ExprStmt
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
attribute [local simp] Compi... | @@ -407,6 +407,48 @@
· simp
· exact hih
+private theorem firstInFieldConflictCopy_ne_none_of_seen_slot_unpacked
+ {seen current : List (Nat × String × Option PackedBits)}
+ {slot : Nat}
+ (hseen : slot ∈ seen.map (fun entry => entry.1))
+ (hcurrent : slot ∈ current.map (fun entry => entr... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_111066ac5beb_0 | 74c8d9b10991847e | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/Core/Uint256.lean | Uint256 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 4 | [
{
"theorem_name": "max_uint256_succ_eq_modulus",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Na... | [
{
"name": "sub_add_cancel",
"text": "theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\n",
"fan_in": 4,
"n_lines": 4,
"n_chars": 98,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n... | [
{
"name": "max_uint256_succ_eq_modulus",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 8,
"n_chars": 333,
"n_subproofs": 3,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 3 | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | @@ -37,7 +37,7 @@
have h2 : (0 : Nat) < (2 : Nat) := by decide
have hle : 1 ≤ (2 ^ 256) := by
exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)
- have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := sorry
+ have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle
simp [MAX_UINT256, modulus, UINT256_... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_111066ac5beb_1 | 7a51c88a91b23a5a | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/Core/Uint256.lean | Uint256 | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 4 | [
{
"theorem_name": "max_uint256_succ_eq_modulus",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Na... | [
{
"name": "sub_add_cancel",
"text": "theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\n",
"fan_in": 4,
"n_lines": 4,
"n_chars": 98,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n... | [
{
"name": "val_le_max",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 11,
"n_chars": 304,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": 8... | 4 | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | @@ -37,7 +37,7 @@
have h2 : (0 : Nat) < (2 : Nat) := by decide
have hle : 1 ≤ (2 ^ 256) := by
exact Nat.succ_le_of_lt (Nat.pow_pos (a := 2) (n := 256) h2)
- have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := sorry
+ have h : (2 ^ 256 - 1) + 1 = 2 ^ 256 := Nat.sub_add_cancel hle
simp [MAX_UINT256, modulus, UINT256_... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_111066ac5beb_2 | 487b7f86647800b3 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/Core/Uint256.lean | Uint256 | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 4 | [
{
"theorem_name": "max_uint256_succ_eq_modulus",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Na... | [
{
"name": "sub_add_cancel",
"text": "theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\n",
"fan_in": 4,
"n_lines": 4,
"n_chars": 98,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n... | [
{
"name": "sub_add_cancel_left",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 7,
"n_lines": 56,
"n_chars": 1950,
"n_subproofs": 8,
"n_tactics": 53,
"cyclomatic": 1,
"n_automation": 13,
"n_rewrites": 0,
"n_structural": 13,
"automation_only": false,
"ma... | 3 | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | @@ -356,12 +356,42 @@
apply ext
let m : Nat := modulus
by_cases h : b.val ≤ a.val
- · sorry
+ · have hlt : a.val - b.val < m := by
+ exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt
+ have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt
+ calc
+ ((a - b) + b).val
+ = (((a.val - b.val) % ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_111066ac5beb_3 | e6bf01f1093df4cb | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/Core/Uint256.lean | Uint256 | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "sub_add_cancel",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n sub_add_cancel_of_lt a.isLt b.isLt",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "sub_add_cancel_of_lt",
"text": "theorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :\n (a + b - b) = a := by\n cases a with\n | mk a ha' =>\n cases b with\n | mk b hb' =>\n apply ext\n let m : Nat := modulus\n have ha'' : a < m := by... | [
{
"name": "sub_add_cancel",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 4,
"n_chars": 98,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 2 | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | @@ -429,8 +429,113 @@
simp [HDiv.hDiv, div, h, ofNat]
_ = 0 := by simp
-theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a := sorry
+theorem sub_add_cancel_of_lt {a b : Uint256} (ha : a.val < modulus) (hb : b.val < modulus) :
+ (a + b - b) = a := by
+ cases a with
+ | mk a ha' =>
+ cases b... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_111066ac5beb_4 | bb4e449acdf0b724 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/Core/Uint256.lean | Uint256 | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 4 | [
{
"theorem_name": "max_uint256_succ_eq_modulus",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h2 : (0 : Nat) < (2 : Nat) := by decide\n have hle : 1 ≤ (2 ^ 256) := by\n exact Nat.succ_le_of_lt (Na... | [
{
"name": "sub_add_cancel",
"text": "theorem sub_add_cancel (a b : Uint256) : (a + b - b) = a :=\n sub_add_cancel_of_lt a.isLt b.isLt\n\n",
"fan_in": 4,
"n_lines": 4,
"n_chars": 98,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n... | [
{
"name": "add_right_cancel",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 10,
"n_chars": 247,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesti... | 3 | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | /-
Core Uint256 Operations
This module provides arithmetic operations with EVM semantics:
- All operations wrap at 2^256 (modular arithmetic)
- Division and modulo by zero return 0 (matches EVM)
- Provides overflow/underflow detection predicates
These operations ensure semantic equivalence between EDSL
... | @@ -356,12 +356,42 @@
apply ext
let m : Nat := modulus
by_cases h : b.val ≤ a.val
- · sorry
+ · have hlt : a.val - b.val < m := by
+ exact Nat.lt_of_le_of_lt (Nat.sub_le _ _) a.isLt
+ have hle : a.val - b.val ≤ m := Nat.le_of_lt hlt
+ calc
+ ((a - b) + b).val
+ = (((a.val - b.val) % ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_0 | bde1c737ba5df7c6 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine { compileOk := hcompile, preserves := ?_ }\n intro runtime ... | [
{
"name": "compileStmt_internalCallAssign_shape_with_internals",
"text": "theorem compileStmt_internalCallAssign_shape_with_internals\n {fields : List CompilationModel.Field}\n {events : List EventDef}\n {errors : List ErrorDef}\n {scope : List String}\n {internalFunctions : List FunctionSpec... | [
{
"name": "compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCallAssign",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 49,
"n_chars": 2982,
"n_subproofs": 8,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 7,
"n_stru... | 1 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Spec-functions-aware constru... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
theorem compileStmt_internalCall... | @@ -10,6 +10,37 @@
open Compiler.CompilationModel
open Compiler.Yul
+theorem compileStmt_internalCallAssign_shape_with_internals
+ {fields : List CompilationModel.Field}
+ {events : List EventDef}
+ {errors : List ErrorDef}
+ {scope : List String}
+ {internalFunctions : List FunctionSpec}
+ {names... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_1 | 33a7fd2ac1c10484 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine { compileOk := hcompile, preserves := ?_ }\n intro runtime state ... | [
{
"name": "compileStmt_internalCall_shape_with_internals",
"text": "theorem compileStmt_internalCall_shape_with_internals\n {fields : List CompilationModel.Field}\n {events : List EventDef}\n {errors : List ErrorDef}\n {scope : List String}\n {internalFunctions : List FunctionSpec}\n {func... | [
{
"name": "compiledStmtStepWithHelpersAndHelperIRWithInternals_internalCall",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 49,
"n_chars": 2884,
"n_subproofs": 8,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 7,
"n_structural... | 1 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Spec-functions-aware constru... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
theorem compileStmt_internalCall... | @@ -10,6 +10,36 @@
open Compiler.CompilationModel
open Compiler.Yul
+theorem compileStmt_internalCall_shape_with_internals
+ {fields : List CompilationModel.Field}
+ {events : List EventDef}
+ {errors : List ErrorDef}
+ {scope : List String}
+ {internalFunctions : List FunctionSpec}
+ {functionNam... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_2 | ce4101ea17d25db3 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n exact\n directInternalHelperHeadStepBridgeCatalog_of... | [
{
"name": "directInternalHelperPerCalleeBridgeCatalog_of_supportedBody_and_assignBridgeCatalog",
"text": "/-- Reassemble the full callee-local bridge catalog from the current supported\nbody witness plus the assign-only bridge half. The call half is vacuous because\n`SupportedStmtList` still excludes direct... | [
{
"name": "directInternalHelperHeadStepBridgeCatalog_of_supportedBody_and_assignBridgeCatalog",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 28,
"n_chars": 1171,
"n_subproofs": 0,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,... | 2 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -281,6 +281,25 @@
calleeName ∈ helperCallNames fn →
DirectInternalHelperAssignHeadStepBridge runtimeContract spec fields calleeName
+/-- Reassemble the full callee-local bridge catalog from the current supported
+body witness plus the assign-only bridge half. The call half is vacuous because
+`Suppor... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_3 | cb08e4831eecb217 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "directInternalHelperHeadStepCatalog_call_of_bridgeCatalog",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) ... | [
{
"name": "compiledStmtStepWithHelpersAndHelperIR_internalCall",
"text": "theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {c... | [
{
"name": "directInternalHelperHeadStepCatalog_call_of_bridgeCatalog",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 48,
"n_chars": 1730,
"n_subproofs": 2,
"n_tactics": 31,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 5,
... | 1 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
theorem compiledStmtStepWithHelp... | @@ -10,6 +10,73 @@
open Compiler.CompilationModel
open Compiler.Yul
+theorem compiledStmtStepWithHelpersAndHelperIR_internalCall
+ {runtimeContract : IRContract}
+ {spec : CompilationModel}
+ {fields : List Field}
+ {scope : List String}
+ {calleeName : String} {args : List Expr}
+ {compiledIR : L... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_4 | 2d7fa8964b45955c | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope ... | [
{
"name": "compiledStmtStepWithHelpersAndHelperIR_internalCallAssign",
"text": "/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction wi... | [
{
"name": "directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 41,
"n_chars": 1612,
"n_subproofs": 2,
"n_tactics": 24,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 5,... | 1 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Constructor for the helper-a... | @@ -10,6 +10,81 @@
open Compiler.CompilationModel
open Compiler.Yul
+/-- Constructor for the helper-aware single-step interface when the head
+statement is `Stmt.internalCallAssign`. The proof is parameterised by a single
+source-to-IR alignment bridge that the rank-decreasing callee induction will
+supply. The bri... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_5 | 9d3735538da801c6 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope ... | [
{
"name": "compiledStmtStepWithHelpersAndHelperIR_internalCallAssign",
"text": "/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction wi... | [
{
"name": "directInternalHelperHeadStepCatalog_of_bridgeCatalog",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 16,
"n_chars": 801,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"aut... | 4 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
theorem compiledStmtStepWithHelp... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Constructor for the helper-a... | @@ -10,6 +10,81 @@
open Compiler.CompilationModel
open Compiler.Yul
+/-- Constructor for the helper-aware single-step interface when the head
+statement is `Stmt.internalCallAssign`. The proof is parameterised by a single
+source-to-IR alignment bridge that the rank-decreasing callee induction will
+supply. The bri... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_6 | 3c34c3ee1cfca0ef | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "directInternalHelperHeadStepCatalog_assign_of_bridgeCatalog",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro scope names calleeName args hmem\n rcases hbridge.assignCompile (scope ... | [
{
"name": "compiledStmtStepWithHelpersAndHelperIR_internalCallAssign",
"text": "/-- Constructor for the helper-aware single-step interface when the head\nstatement is `Stmt.internalCallAssign`. The proof is parameterised by a single\nsource-to-IR alignment bridge that the rank-decreasing callee induction wi... | [
{
"name": "directInternalHelperHeadStepCatalog_of_perCalleeBridgeCatalog",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 25,
"n_chars": 1044,
"n_subproofs": 0,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": ... | 6 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
theorem compiledStmtStepWithHelp... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Constructor for the helper-a... | @@ -10,6 +10,81 @@
open Compiler.CompilationModel
open Compiler.Yul
+/-- Constructor for the helper-aware single-step interface when the head
+statement is `Stmt.internalCallAssign`. The proof is parameterised by a single
+source-to-IR alignment bridge that the rank-decreasing callee induction will
+supply. The bri... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_7 | 672800b91532c096 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "directInternalHelperHeadStepCatalog_call_of_bridgeCatalog",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro scope calleeName args hmem\n rcases hbridge.callCompile (scope := scope) ... | [
{
"name": "compiledStmtStepWithHelpersAndHelperIR_internalCall",
"text": "theorem compiledStmtStepWithHelpersAndHelperIR_internalCall\n {runtimeContract : IRContract}\n {spec : CompilationModel}\n {fields : List Field}\n {scope : List String}\n {calleeName : String} {args : List Expr}\n {c... | [
{
"name": "directInternalHelperHeadStepCatalog_of_supportedBody_and_assignBridgeCatalog",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 8,
"n_lines": 28,
"n_chars": 1096,
"n_subproofs": 0,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"... | 8 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Constructor for the helper-a... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Constructor for the helper-a... | @@ -85,6 +85,73 @@
rw [hFuelEq]
exact ⟨_, _, rfl, rfl, hMatch⟩
+theorem compiledStmtStepWithHelpersAndHelperIR_internalCall
+ {runtimeContract : IRContract}
+ {spec : CompilationModel}
+ {fields : List Field}
+ {scope : List String}
+ {calleeName : String} {args : List Expr}
+ {compiledIR : Li... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_8 | bb11eb2e42eabf20 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "List.mem_eraseDups_iff_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a",
"n_chars": 69,
"n_subproofs": 0,
... | [
{
"name": "eraseDups_nodup_and_mem_aux_local",
"text": "private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l ... | [
{
"name": "List.mem_eraseDups_iff_local",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 201,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -312,8 +312,51 @@
CompilationModel.compileStmt fields [] [] .calldata [] false scope []
(Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR
+private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]
+ (n : Nat) (l : List α) (hlen : l.length ≤ n) :
+ (l... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_9 | 9a5348957a453fcb | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "List.mem_eraseDups_iff_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a",
"n_chars": 69,
"n_subproofs": 0,
... | [
{
"name": "eraseDups_nodup_and_mem_aux_local",
"text": "private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l ... | [
{
"name": "List.mem_eraseDups_of_mem_local",
"fan_in": 6,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 174,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 2 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -312,8 +312,51 @@
CompilationModel.compileStmt fields [] [] .calldata [] false scope []
(Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR
+private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]
+ (n : Nat) (l : List α) (hlen : l.length ≤ n) :
+ (l... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_10 | c7feacdc436bfb62 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "List.mem_eraseDups_iff_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a",
"n_chars": 69,
"n_subproofs": 0,
... | [
{
"name": "eraseDups_nodup_and_mem_aux_local",
"text": "private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]\n (n : Nat) (l : List α) (hlen : l.length ≤ n) :\n (l.eraseDups).Nodup ∧ (∀ a, a ∈ l.eraseDups ↔ a ∈ l) := by\n induction n generalizing l with\n | zero =>\n have : l ... | [
{
"name": "List.mem_of_mem_eraseDups_local",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 173,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 2 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -312,8 +312,51 @@
CompilationModel.compileStmt fields [] [] .calldata [] false scope []
(Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR
+private theorem eraseDups_nodup_and_mem_aux_local [BEq α] [LawfulBEq α]
+ (n : Nat) (l : List α) (hlen : l.length ≤ n) :
+ (l... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_11 | e545161a59d2cff9 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 2 | [
{
"theorem_name": "List.mem_eraseDups_of_mem_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n List.mem_eraseDups_iff_local.mpr h",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "List.mem_eraseDups_iff_local",
"text": "private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 201,
... | [
{
"name": "internalCallAssign_callee_mem_stmtListInternalHelperCallNames_eraseDups",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 426,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_struct... | 3 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -354,8 +354,13 @@
· exact Or.inl (beq_iff_eq.mp heq)
· exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))
+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]
+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=
+ (eraseDups_nodup_and_mem_aux_l... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_12 | 3d16e9a01f47c819 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 2 | [
{
"theorem_name": "List.mem_eraseDups_of_mem_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n List.mem_eraseDups_iff_local.mpr h",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "List.mem_eraseDups_iff_local",
"text": "private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 201,
... | [
{
"name": "internalCall_callee_mem_stmtListInternalHelperCallNames_eraseDups",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 386,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural":... | 3 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -354,8 +354,13 @@
· exact Or.inl (beq_iff_eq.mp heq)
· exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))
+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]
+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=
+ (eraseDups_nodup_and_mem_aux_l... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_13 | 2e174c74ec950127 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 2 | [
{
"theorem_name": "List.mem_eraseDups_of_mem_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n List.mem_eraseDups_iff_local.mpr h",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "List.mem_eraseDups_iff_local",
"text": "private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 201,
... | [
{
"name": "stmtListDirectInternalHelperAssignStepInterface_of_internalCallAssignSteps_of_helperCallNames",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 47,
"n_chars": 2126,
"n_subproofs": 1,
"n_tactics": 26,
"cyclomatic": 4,
"n_automation": 1,
"n_re... | 6 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -354,11 +354,17 @@
· exact Or.inl (beq_iff_eq.mp heq)
· exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))
+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]
+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=
+ (eraseDups_nodup_and_mem_aux_... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_14 | 104c98436ee856c5 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 2 | [
{
"theorem_name": "List.mem_eraseDups_of_mem_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n List.mem_eraseDups_iff_local.mpr h",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "List.mem_eraseDups_iff_local",
"text": "private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 201,
... | [
{
"name": "stmtListDirectInternalHelperAssignStepInterfaceWithInternals_of_internalCallAssignSteps_of_helperCallNames",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 45,
"n_chars": 1994,
"n_subproofs": 1,
"n_tactics": 26,
"cyclomatic": 4,
"n_automation":... | 6 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -354,11 +354,17 @@
· exact Or.inl (beq_iff_eq.mp heq)
· exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))
+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]
+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=
+ (eraseDups_nodup_and_mem_aux_... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_15 | dca9d33483f4947f | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 2 | [
{
"theorem_name": "List.mem_eraseDups_of_mem_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n List.mem_eraseDups_iff_local.mpr h",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "List.mem_eraseDups_iff_local",
"text": "private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 201,
... | [
{
"name": "stmtListDirectInternalHelperCallStepInterface_of_internalCallSteps_of_helperCallNames",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 46,
"n_chars": 2013,
"n_subproofs": 1,
"n_tactics": 25,
"cyclomatic": 4,
"n_automation": 1,
"n_rewrites":... | 6 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -354,11 +354,17 @@
· exact Or.inl (beq_iff_eq.mp heq)
· exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))
+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]
+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=
+ (eraseDups_nodup_and_mem_aux_... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_16 | b78fb7a5bef50c60 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 2 | [
{
"theorem_name": "List.mem_eraseDups_of_mem_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n List.mem_eraseDups_iff_local.mpr h",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "List.mem_eraseDups_iff_local",
"text": "private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 201,
... | [
{
"name": "stmtListDirectInternalHelperCallStepInterfaceWithInternals_of_internalCallSteps_of_helperCallNames",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 44,
"n_chars": 1872,
"n_subproofs": 1,
"n_tactics": 25,
"cyclomatic": 4,
"n_automation": 1,
... | 6 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -354,11 +354,17 @@
· exact Or.inl (beq_iff_eq.mp heq)
· exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))
+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]
+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=
+ (eraseDups_nodup_and_mem_aux_... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_17 | 99b3a9cabb76dc6e | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 2 | [
{
"theorem_name": "List.mem_eraseDups_of_mem_local",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n List.mem_eraseDups_iff_local.mpr h",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "List.mem_eraseDups_iff_local",
"text": "private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]\n {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=\n (eraseDups_nodup_and_mem_aux_local l.length l (Nat.le_refl _)).2 a\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 201,
... | [
{
"name": "stmtListDirectInternalHelperStepInterfaces_of_headStepCatalog",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 42,
"n_chars": 1358,
"n_subproofs": 0,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": ... | 9 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -354,11 +354,17 @@
· exact Or.inl (beq_iff_eq.mp heq)
· exact Or.inr ((ihMem a).mpr (List.mem_filter.mpr ⟨h, by simp [heq]⟩))
+private theorem List.mem_eraseDups_iff_local [BEq α] [LawfulBEq α]
+ {a : α} {l : List α} : a ∈ l.eraseDups ↔ a ∈ l :=
+ (eraseDups_nodup_and_mem_aux_... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_cdb08728ad51_18 | 19c614555363a7ab | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/GenericInduction/Calls.lean | Calls | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 24 | 1 | [
{
"theorem_name": "execIRStmtsWithInternals_of_internalCall_compiledHelperWitness",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hcalleeName : compiledHelper.sourceWitness.callee.name = calleeName :=... | [
{
"name": "internalFunctionYulName_ne_stop",
"text": "private theorem internalFunctionYulName_ne_stop\n (calleeName : String) :\n CompilationModel.internalFunctionYulName calleeName ≠ \"stop\" := by\n intro hEq\n have hHead := congrArg (fun s => s.toList.head?) hEq\n simp [CompilationModel.internal... | [
{
"name": "execIRStmtsWithInternals_of_internalCall_compiledHelperWitness",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 5,
"n_lines": 80,
"n_chars": 3196,
"n_subproofs": 2,
"n_tactics": 42,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 0,
"n_structural":... | 5 | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | import Compiler.Proofs.IRGeneration.GenericInduction.Core
set_option linter.unnecessarySeqFocus false
set_option linter.unnecessarySimpa false
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
open Compiler.Yul
/-- Exact Tier 4 head-step proof... | @@ -312,6 +312,20 @@
CompilationModel.compileStmt fields [] [] .calldata [] false scope []
(Stmt.internalCallAssign names calleeName args) = Except.ok compiledIR
+private theorem internalFunctionYulName_ne_stop
+ (calleeName : String) :
+ CompilationModel.internalFunctionYulName calleeNa... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_4b939bb4e6c3_0 | 5cd6f2ec043f4cef | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/Core/Int256.lean | Int256 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "minValue_le",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n · have hge : signBit ≤ value.word.val := N... | [
{
"name": "modulus_eq_two_mul_signBit",
"text": "theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\n native_decide\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 82,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_str... | [
{
"name": "minValue_le",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 365,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 4... | 1 | import Verity.Core.Uint256
namespace Verity.Core
structure Int256 where
word : Uint256
deriving DecidableEq
namespace Int256
def modulus : Nat := Uint256.modulus
def signBit : Nat := 2 ^ 255
def minValue : Int := -Int.ofNat signBit
def maxValue : Int := Int.ofNat signBit - 1
def ofUint256 (value : Uint256) ... | import Verity.Core.Uint256
namespace Verity.Core
structure Int256 where
word : Uint256
deriving DecidableEq
namespace Int256
def modulus : Nat := Uint256.modulus
def signBit : Nat := 2 ^ 255
def minValue : Int := -Int.ofNat signBit
def maxValue : Int := Int.ofNat signBit - 1
def ofUint256 (value : Uint256) ... | @@ -63,10 +63,16 @@
have h' : ¬ value.word.val < signBit := Nat.not_lt_of_ge h
simp [Int256.toInt, h']
+theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by
+ native_decide
+
theorem minValue_le (value : Int256) : minValue ≤ (value : Int) := by
by_cases h : value.word.val < signBit
· simp [t... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_4b939bb4e6c3_1 | 5a2d9e2b90ebbfae | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/Core/Int256.lean | Int256 | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "minValue_le",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases h : value.word.val < signBit\n · simp [toInt_of_lt_signBit h, minValue]\n · have hge : signBit ≤ value.word.val := N... | [
{
"name": "modulus_eq_two_mul_signBit",
"text": "theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by\n native_decide\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 82,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_str... | [
{
"name": "toInt_in_range",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 4,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 3 | import Verity.Core.Uint256
namespace Verity.Core
structure Int256 where
word : Uint256
deriving DecidableEq
namespace Int256
def modulus : Nat := Uint256.modulus
def signBit : Nat := 2 ^ 255
def minValue : Int := -Int.ofNat signBit
def maxValue : Int := Int.ofNat signBit - 1
def ofUint256 (value : Uint256) ... | import Verity.Core.Uint256
namespace Verity.Core
structure Int256 where
word : Uint256
deriving DecidableEq
namespace Int256
def modulus : Nat := Uint256.modulus
def signBit : Nat := 2 ^ 255
def minValue : Int := -Int.ofNat signBit
def maxValue : Int := Int.ofNat signBit - 1
def ofUint256 (value : Uint256) ... | @@ -63,10 +63,16 @@
have h' : ¬ value.word.val < signBit := Nat.not_lt_of_ge h
simp [Int256.toInt, h']
+theorem modulus_eq_two_mul_signBit : modulus = 2 * signBit := by
+ native_decide
+
theorem minValue_le (value : Int256) : minValue ≤ (value : Int) := by
by_cases h : value.word.val < signBit
· simp [t... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_72489ced2f65_0 | 02dba1d78c8e3651 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/YulGeneration/Backends/EvmYulLeanPureBuiltinLemmas.lean | EvmYulLeanPureBuiltinLemmas | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "slt_int256_eq_sltBool",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold EvmYul.UInt256.slt\n rw [toNat_fromBool]\n unfold EvmYul.UInt256.sltBool\n simp only [EvmYul.UInt256.toNat... | [
{
"name": "toNat_fromBool",
"text": "private theorem toNat_fromBool (b : Bool) :\n EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by\n cases b <;> rfl\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 134,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_autom... | [
{
"name": "slt_int256_eq_sltBool",
"fan_in": 1,
"n_deps_direct": 9,
"n_deps_transitive": 3,
"n_lines": 22,
"n_chars": 1144,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 3,
"n_automation": 7,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"ma... | 2 | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas
import Mathlib.Data.Nat.Bitwise
import Verity.Core.Int256
import Verity.Core.Uint256
namespace Compiler.Proofs.YulGeneration.Backends
private theorem uint256_size_eq_e... | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas
import Mathlib.Data.Nat.Bitwise
import Verity.Core.Int256
import Verity.Core.Uint256
namespace Compiler.Proofs.YulGeneration.Backends
private theorem uint256_size_eq_e... | @@ -104,6 +104,10 @@
rw [← uint256_size_eq_evmModulus]
rfl
+private theorem toNat_fromBool (b : Bool) :
+ EvmYul.UInt256.toNat (Bool.toUInt256 b) = if b then 1 else 0 := by
+ cases b <;> rfl
+
private theorem uint256_lt_iff_nat_lt {a b : Nat}
(ha : a < EvmYul.UInt256.size) (hb : b < EvmYul.UInt256.siz... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_72489ced2f65_1 | 68b0dd09ec3a777a | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/YulGeneration/Backends/EvmYulLeanPureBuiltinLemmas.lean | EvmYulLeanPureBuiltinLemmas | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "evalPureBuiltinViaEvmYulLean_or_native",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← uint256_size_eq_evmModulus]\n change some (((Nat.bitwise Bool.or (a % EvmYul.UInt256.size) (b... | [
{
"name": "word_lt_uint256_size",
"text": "private theorem word_lt_uint256_size (x : Nat) :\n x % EvmYul.UInt256.size < 2 ^ 256 := by\n simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
... | [
{
"name": "evalPureBuiltinViaEvmYulLean_or_native",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 600,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 1,
"automation_only":... | 1 | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas
import Mathlib.Data.Nat.Bitwise
import Verity.Core.Int256
import Verity.Core.Uint256
namespace Compiler.Proofs.YulGeneration.Backends
private theorem uint256_size_eq_e... | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas
import Mathlib.Data.Nat.Bitwise
import Verity.Core.Int256
import Verity.Core.Uint256
namespace Compiler.Proofs.YulGeneration.Backends
private theorem uint256_size_eq_e... | @@ -10,6 +10,10 @@
EvmYul.UInt256.size = Compiler.Constants.evmModulus := by
decide
+private theorem word_lt_uint256_size (x : Nat) :
+ x % EvmYul.UInt256.size < 2 ^ 256 := by
+ simpa [EvmYul.UInt256.size] using Nat.mod_lt x (by decide : 0 < EvmYul.UInt256.size)
+
@[simp] theorem evalPureBuiltinViaEvmYul... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_72489ced2f65_2 | 519da257b383f582 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/YulGeneration/Backends/EvmYulLeanPureBuiltinLemmas.lean | EvmYulLeanPureBuiltinLemmas | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "evalPureBuiltinViaEvmYulLean_not_native",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← uint256_size_eq_evmModulus]\n change evalPureBuiltinViaEvmYulLean \"not\" [a] =\n some (... | [
{
"name": "xor_all_ones_uint256_word",
"text": "private theorem xor_all_ones_uint256_word (a : Nat) :\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by\n calc\n (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =\n ... | [
{
"name": "evalPureBuiltinViaEvmYulLean_not_native",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 36,
"n_chars": 1766,
"n_subproofs": 7,
"n_tactics": 31,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 8,
"n_structural": 2,
"automation_onl... | 1 | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas
import Mathlib.Data.Nat.Bitwise
import Verity.Core.Int256
import Verity.Core.Uint256
namespace Compiler.Proofs.YulGeneration.Backends
private theorem uint256_size_eq_e... | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeLowering
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanNativeSignedArithLemmas
import Mathlib.Data.Nat.Bitwise
import Verity.Core.Int256
import Verity.Core.Uint256
namespace Compiler.Proofs.YulGeneration.Backends
private theorem uint256_size_eq_e... | @@ -429,10 +429,52 @@
rw [Nat.mod_eq_of_lt]
exact Nat.xor_lt_two_pow (word_lt_uint256_size a) (word_lt_uint256_size b)
+private theorem xor_all_ones_uint256_word (a : Nat) :
+ (a % EvmYul.UInt256.size) ^^^ (EvmYul.UInt256.size - 1) =
+ EvmYul.UInt256.size - 1 - (a % EvmYul.UInt256.size) := by
+ calc
+ ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_5f3c738a4fec_0 | 471501b8c4ba359e | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/CEISafety.lean | CEISafety | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "ceiProofBackedExecution_checked_empty_body",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n by\n refine ceiProofBackedExecution_of_checker rfl ?_ rfl rfl rfl\n change stmtListCEIViolati... | [
{
"name": "ceiProofBackedExecution_of_checker",
"text": "/-- Bridge the concrete facts emitted by the macro/checker into the public CEI\nexecution theorem. Escape hatches are hypotheses rather than hidden premises. -/\ntheorem ceiProofBackedExecution_of_checker\n {fn : FunctionSpec}\n (hAnnotated : fn... | [
{
"name": "ceiProofBackedExecution_checked_empty_body",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 548,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 1,
"automation_on... | 1 | import Compiler.CompilationModel.Validation
/-!
Proof-layer CEI safety surface.
`stmtListCEIViolation` is the compiler checker used before code generation.
This module gives that checker a public proof-facing meaning: a function has
proof-backed CEI execution safety exactly when the checker accepts its body and
the r... | import Compiler.CompilationModel.Validation
/-!
Proof-layer CEI safety surface.
`stmtListCEIViolation` is the compiler checker used before code generation.
This module gives that checker a public proof-facing meaning: a function has
proof-backed CEI execution safety exactly when the checker accepts its body and
the r... | @@ -43,6 +43,23 @@
executionSafe : CEIExecutionSafe fn
trustExitsClosed : CEITrustExitsClosed fn
+/-- Bridge the concrete facts emitted by the macro/checker into the public CEI
+execution theorem. Escape hatches are hypotheses rather than hidden premises. -/
+theorem ceiProofBackedExecution_of_checker
+ {fn ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_81701029c1fb_0 | c06abb9f27def0da | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean | Safe | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "bridgedSafeStmts_assignKeccak_of_exprCompileCore",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n BridgedSafeStmts.storage (by\n intro stmt hMem\n simp only [List.mem_singleton] at hMem... | [
{
"name": "bridgedSourcePureBindingStmt_assignKeccak_of_exprCompileCore",
"text": "/-- An assignment whose RHS is syntactic `keccak256(offset, size)` is a native\n pure-binding source statement when the offset and size arguments are\n compile-core expressions. -/\ntheorem bridgedSourcePureBindingStmt_... | [
{
"name": "bridgedSafeStmts_assignKeccak_of_exprCompileCore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 930,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automat... | 1 | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | @@ -172,6 +172,20 @@
BridgedSourcePureBindingStmt.letVar name (.keccak256 offset size)
(bridgedSourceExpr_keccak256_of_exprCompileCore hOffset hSize)
+/-- An assignment whose RHS is syntactic `keccak256(offset, size)` is a native
+ pure-binding source statement when the offset and size arguments are
+ c... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_81701029c1fb_1 | 7e86793a38eea6c2 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean | Safe | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction hTerminal with\n | letVar hValue _hScope _hRest ih =>... | [
{
"name": "bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore",
"text": "/-- Source compile-core statement lists are covered by the recursive external\n raw-log fragment: pure bindings route through the storage/body base\n predicate, requires and terminators are direct body cases... | [
{
"name": "bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 38,
"n_chars": 1848,
"n_subproofs": 0,
"n_tactics": 24,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_s... | 1 | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | @@ -273,6 +273,36 @@
dynamicSource (.ite cond thenBranch elseBranch) :=
.ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse
+/-- Source compile-core statement lists are covered by the recursive external
+ raw-log fragment: pure bindings route through the storage/body base
+ predicate, ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_81701029c1fb_2 | 7bdff3781f9cde0a | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean | Safe | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction hTerminal with\n | letVar hValue _hScope _hRest ih =>... | [
{
"name": "bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListCompileCore",
"text": "/-- Source compile-core statement lists are covered by the recursive external\n raw-log fragment: pure bindings route through the storage/body base\n predicate, requires and terminators are direct body cases... | [
{
"name": "bridgedSafeStmts_externalCompileCore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 724,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": f... | 1 | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | @@ -273,6 +273,36 @@
dynamicSource (.ite cond thenBranch elseBranch) :=
.ite _ _ _ (bridgedSourceExpr_of_exprCompileCore hCond) hThen hElse
+/-- Source compile-core statement lists are covered by the recursive external
+ raw-log fragment: pure bindings route through the storage/body base
+ predicate, ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_81701029c1fb_3 | 18cbde08d7ee74e3 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean | Safe | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "bridgedSafeStmts_externalTerminalCore",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n BridgedSafeStmts.externalRecursiveRawLog\n (bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmt... | [
{
"name": "bridgedSourceExternalRecursiveBodyWithRawLogStmts_of_stmtListTerminalCore",
"text": "/-- Terminal compile-core statement lists have the same external native source\n coverage as ordinary compile-core lists. The terminal `return`/`stop` cases\n delegate their tails to the compile-core bridge... | [
{
"name": "bridgedSafeStmts_externalTerminalCore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 649,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": ... | 2 | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | @@ -303,6 +303,43 @@
| tstore hOffset _hOffsetScope hValue _hValueScope _hRest ih =>
exact .cons (bridgedExternalRawLogTstore hOffset hValue) ih
+/-- Terminal compile-core statement lists have the same external native source
+ coverage as ordinary compile-core lists. The terminal `return`/`stop` cases
+ ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_81701029c1fb_4 | 9321d0d544957037 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/YulGeneration/Backends/EvmYulLeanBodyClosure/Safe.lean | Safe | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "BridgedSafeStmts.toBridgedSource",
"depth": 1,
"n_commands": 0,
"n_lines": 88,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction hSafe with\n | externalRecursiveRawLog hStmts =>\n exact fun stmt hMem => .externalRecurs... | [
{
"name": "mem_of_internalRecursiveRawLogStmts",
"text": "private theorem mem_of_internalRecursiveRawLogStmts\n {fields : List Field} {errors : List ErrorDef}\n {dynamicSource : DynamicDataSource} :\n ∀ (stmts : List Stmt),\n BridgedSourceInternalRecursiveBodyWithRawLogStmts fields errors\n ... | [
{
"name": "BridgedSafeStmts.toBridgedSource",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 103,
"n_chars": 4965,
"n_subproofs": 0,
"n_tactics": 88,
"cyclomatic": 3,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 44,
"automation_only": f... | 2 | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Base
import Compiler.Proofs.YulGeneration.Backends.EvmYulLeanBodyClosure.Generic
set_option linter.unusedSimpArgs false
namespace Compiler.Proofs.YulGeneration.Backends
open Compiler
open Compiler.Yul
open Compiler.CompilationModel
open Compiler.Pro... | @@ -293,6 +293,26 @@
| head => exact hHead
| tail _ hMem => exact ih hTail stmt hMem
+private theorem mem_of_internalRecursiveRawLogStmts
+ {fields : List Field} {errors : List ErrorDef}
+ {dynamicSource : DynamicDataSource} :
+ ∀ (stmts : List Stmt),
+ BridgedSourceInternalRecursi... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_bc040358e506_0 | 856e1b61aeb1017e | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Contracts/Smoke/EIP712StaticSmoke.lean | EIP712StaticSmoke | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "permitStaticHash_eip712Supported_and_digest_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · exact permitStaticHashAndDigest_supported\n · constructor\n · con... | [
{
"name": "permitStaticHashAndDigest_supported",
"text": "private theorem permitStaticHashAndDigest_supported :\n SupportedStmtList [] permitScope permitStaticHashAndDigestStmts := by\n change SupportedStmtList [] permitScope ([permitStructHashStmt] ++ [permitDigestStmt])\n apply SupportedStmtList.appe... | [
{
"name": "permitStaticHash_eip712Supported_and_digest_correct",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 572,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 5,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 7,
"aut... | 1 | import Contracts.Common
import Compiler.Modules.Hashing
import Compiler.Proofs.IRGeneration.SupportedSpec
namespace Contracts.Smoke
open Compiler
open Compiler.CompilationModel
open Compiler.Proofs.IRGeneration
open Compiler.Yul
open Verity hiding pure bind
def permitTypeHash : Nat :=
(keccakString "Permit(address... | import Contracts.Common
import Compiler.Modules.Hashing
import Compiler.Proofs.IRGeneration.SupportedSpec
namespace Contracts.Smoke
open Compiler
open Compiler.CompilationModel
open Compiler.Proofs.IRGeneration
open Compiler.Yul
open Verity hiding pure bind
def permitTypeHash : Nat :=
(keccakString "Permit(address... | @@ -62,12 +62,40 @@
[YulExpr.ident "domainSeparator", YulExpr.ident "structHash"] =
Except.ok Compiler.Modules.Hashing.eip712DigestExpectedYul
+private theorem permitStaticHashAndDigest_supported :
+ SupportedStmtList [] permitScope permitStaticHashAndDigestStmts := by
+ change SupportedStmtList [] pe... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_bd1f7089f857_0 | fe19b59a09e8928b | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/EVM/Frame.lean | Frame | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "external_call_preserves_caller_memory",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply external_call_preserves_caller_memory_outside_output_buffer\n rintro ⟨h1, h2⟩\n rcases hDisj ... | [
{
"name": "external_call_preserves_caller_memory_outside_output_buffer",
"text": "theorem external_call_preserves_caller_memory_outside_output_buffer\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (i : Nat) (hOutside : ¬ (outOff ≤ i ∧ i < outOff + outSize)) :\n (applyCall... | [
{
"name": "external_call_preserves_caller_memory",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 669,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": ... | 1 | import Verity.EVM.Uint256
import Verity.EVM.MemoryModel
import Verity.Core.Uint256
namespace Verity.EVM.Frame
open Verity.Core (Uint256)
open Verity.EVM.MemoryModel
/-!
# EVM `CALL` boundary frame conditions
Models the slice of EVM `CALL` semantics that touches the caller's
frame, and proves the frame conditions th... | import Verity.EVM.Uint256
import Verity.EVM.MemoryModel
import Verity.Core.Uint256
namespace Verity.EVM.Frame
open Verity.Core (Uint256)
open Verity.EVM.MemoryModel
/-!
# EVM `CALL` boundary frame conditions
Models the slice of EVM `CALL` semantics that touches the caller's
frame, and proves the frame conditions th... | @@ -79,6 +79,13 @@
/-! ## Single-CALL frame theorems -/
+theorem external_call_preserves_caller_memory_outside_output_buffer
+ (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)
+ (i : Nat) (hOutside : ¬ (outOff ≤ i ∧ i < outOff + outSize)) :
+ (applyCallToCaller caller outOff outSize c... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_bd1f7089f857_1 | 2374913f63f8213c | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/EVM/Frame.lean | Frame | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "external_calls_preserve_caller_storage",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n have hStep := e... | [
{
"name": "external_call_preserves_caller_storage",
"text": "theorem external_call_preserves_caller_storage\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (slotIdx : Nat) :\n (applyCallToCaller caller outOff outSize callee).storageMap slotIdx =\n caller.storageMap sl... | [
{
"name": "external_calls_preserve_caller_storage",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 548,
"n_subproofs": 2,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only":... | 1 | import Verity.EVM.Uint256
import Verity.EVM.MemoryModel
import Verity.Core.Uint256
namespace Verity.EVM.Frame
open Verity.Core (Uint256)
open Verity.EVM.MemoryModel
/-!
# EVM `CALL` boundary frame conditions
Models the slice of EVM `CALL` semantics that touches the caller's
frame, and proves the frame conditions th... | import Verity.EVM.Uint256
import Verity.EVM.MemoryModel
import Verity.Core.Uint256
namespace Verity.EVM.Frame
open Verity.Core (Uint256)
open Verity.EVM.MemoryModel
/-!
# EVM `CALL` boundary frame conditions
Models the slice of EVM `CALL` semantics that touches the caller's
frame, and proves the frame conditions th... | @@ -79,13 +79,26 @@
/-! ## Single-CALL frame theorems -/
+theorem external_call_preserves_caller_storage
+ (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)
+ (slotIdx : Nat) :
+ (applyCallToCaller caller outOff outSize callee).storageMap slotIdx =
+ caller.storageMap slotIdx := b... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_bd1f7089f857_2 | c8321e8396fe53a4 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/EVM/Frame.lean | Frame | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "external_calls_preserve_caller_transient_storage",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n have ... | [
{
"name": "external_call_preserves_caller_transient_storage",
"text": "theorem external_call_preserves_caller_transient_storage\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)\n (slotIdx : Nat) :\n (applyCallToCaller caller outOff outSize callee).transientStorage slotIdx =\n... | [
{
"name": "external_calls_preserve_caller_transient_storage",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 586,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automat... | 1 | import Verity.EVM.Uint256
import Verity.EVM.MemoryModel
import Verity.Core.Uint256
namespace Verity.EVM.Frame
open Verity.Core (Uint256)
open Verity.EVM.MemoryModel
/-!
# EVM `CALL` boundary frame conditions
Models the slice of EVM `CALL` semantics that touches the caller's
frame, and proves the frame conditions th... | import Verity.EVM.Uint256
import Verity.EVM.MemoryModel
import Verity.Core.Uint256
namespace Verity.EVM.Frame
open Verity.Core (Uint256)
open Verity.EVM.MemoryModel
/-!
# EVM `CALL` boundary frame conditions
Models the slice of EVM `CALL` semantics that touches the caller's
frame, and proves the frame conditions th... | @@ -79,13 +79,27 @@
/-! ## Single-CALL frame theorems -/
+theorem external_call_preserves_caller_transient_storage
+ (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeResult)
+ (slotIdx : Nat) :
+ (applyCallToCaller caller outOff outSize callee).transientStorage slotIdx =
+ caller.transie... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_bd1f7089f857_3 | ce39bb8129d53b34 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Verity/EVM/Frame.lean | Frame | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "external_calls_preserve_caller_memory_in_disjoint_region",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction calls generalizing caller with\n | nil => rfl\n | cons c rest ih =>\n... | [
{
"name": "external_call_preserves_caller_memory",
"text": "/-- Headline form: caller-memory preservation under a disjoint output\n buffer. Composes directly with `MemoryModel.Disjoint`. -/\ntheorem external_call_preserves_caller_memory\n (caller : CallerFrame) (outOff outSize : Nat) (callee : CalleeR... | [
{
"name": "external_calls_preserve_caller_memory_in_disjoint_region",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 21,
"n_chars": 919,
"n_subproofs": 3,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 3,
... | 2 | import Verity.EVM.Uint256
import Verity.EVM.MemoryModel
import Verity.Core.Uint256
namespace Verity.EVM.Frame
open Verity.Core (Uint256)
open Verity.EVM.MemoryModel
/-!
# EVM `CALL` boundary frame conditions
Models the slice of EVM `CALL` semantics that touches the caller's
frame, and proves the frame conditions th... | import Verity.EVM.Uint256
import Verity.EVM.MemoryModel
import Verity.Core.Uint256
namespace Verity.EVM.Frame
open Verity.Core (Uint256)
open Verity.EVM.MemoryModel
/-!
# EVM `CALL` boundary frame conditions
Models the slice of EVM `CALL` semantics that touches the caller's
frame, and proves the frame conditions th... | @@ -86,6 +86,21 @@
caller.memory i := by
simp [applyCallToCaller, hOutside]
+/-- Headline form: caller-memory preservation under a disjoint output
+ buffer. Composes directly with `MemoryModel.Disjoint`. -/
+theorem external_call_preserves_caller_memory
+ (caller : CallerFrame) (outOff outSize : Nat) ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_0 | 70cfd87882fb4b8b | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "compileGuardedFunctionSpec_eq_of_none",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold compileGuardedFunctionSpec\n cases hcomp : compileFunctionSpec fields events errors adtTypes ... | [
{
"name": "attachNonReentrantGuard_eq_of_none",
"text": "/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the\nguarded per-function compile in `compileValidatedCore` collapses to the plain\n`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/\ntheorem attachNonReentr... | [
{
"name": "compileGuardedFunctionSpec_eq_of_none",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 821,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": ... | 1 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
theorem compileGuardedFunctionSpec_eq_of_none
(fields : List Field) (events : List EventDef) (errors : List Er... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the
guarded per-function compile in `com... | @@ -9,6 +9,15 @@
namespace ContractShape
+/-- `attachNonReentrantGuard` is the identity for lock-free functions, so the
+guarded per-function compile in `compileValidatedCore` collapses to the plain
+`compileFunctionSpec` mapM on the supported (lock-free) fragment. -/
+theorem attachNonReentrantGuard_eq_of_none
+ ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_1 | a8a317099699e124 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compileValidatedCore_ok_yields_compiled_functions",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 59,
"n_chars": 2702,
"n_subproofs": 5,
"n_tactics": 47,
"cyclomatic": 5,
"n_automation": 10,
"n_rewrites": 2,
"n_structural": 4,
"aut... | 4 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -103,6 +103,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.funct... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_2 | 9d4d6462ae1b3bc1 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compileValidatedCore_ok_yields_internalFunctions_nil",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 50,
"n_chars": 2591,
"n_subproofs": 8,
"n_tactics": 42,
"cyclomatic": 4,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 3,
"a... | 3 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -72,6 +72,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.functio... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_3 | 0b55f116f61022bc | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compileValidatedCore_ok_yields_deploy_compileConstructor",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 42,
"n_chars": 1921,
"n_subproofs": 3,
"n_tactics": 33,
"cyclomatic": 5,
"n_automation": 8,
"n_rewrites": 2,
"n_structural": 4,
... | 3 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -72,6 +72,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.functio... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_4 | 7ef0bef0ddf0d047 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compileValidatedCore_ok_yields_noFallbackEntrypoint",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 39,
"n_chars": 1991,
"n_subproofs": 3,
"n_tactics": 31,
"cyclomatic": 4,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 3,
"au... | 3 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -72,6 +72,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.functio... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_5 | 80f600c95a01e280 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compileValidatedCore_ok_yields_noReceiveEntrypoint",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 39,
"n_chars": 1989,
"n_subproofs": 3,
"n_tactics": 31,
"cyclomatic": 4,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 3,
"aut... | 3 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -72,6 +72,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.functio... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_6 | f3d2f5d9dc479255 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compile_ok_yields_compiled_functions",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 24,
"n_chars": 911,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": ... | 5 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -103,6 +103,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.funct... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_7 | 7e427c333e3e520e | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 6 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "pickUniqueFunctionByName_eq_ok_none_of_absent",
"text": "private theorem pickUniqueFunctionByName_eq_ok_none_of_absent\n (name : String) (funcs : List FunctionSpec)\n (habsent : ∀ fn ∈ funcs, fn.name != name) :\n pickUniqueFunctionByName name funcs = Except.ok none := by\n induction fun... | [
{
"name": "compileValidatedCore_ok_yields_compiled_functions_with_scalar_events",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 46,
"n_chars": 2236,
"n_subproofs": 5,
"n_tactics": 34,
"cyclomatic": 5,
"n_automation": 9,
"n_rewrites": 2,
"n_struct... | 3 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem compiled_functions_forall₂_of_mapM_ok
(fields : List Field)
(events : List EventDef)
(... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -9,6 +9,25 @@
namespace ContractShape
+private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
+ (name : String) (funcs : List FunctionSpec)
+ (habsent : ∀ fn ∈ funcs, fn.name != name) :
+ pickUniqueFunctionByName name funcs = Except.ok none := by
+ induction funcs with
+ | nil =>
+ rfl
+ ... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_8 | e04b168bca979f39 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "compiled_functions_forall₂_of_mapM_ok",
"text": "private theorem compiled_functions_forall₂_of_mapM_ok\n (fields : List Field)\n (events : List EventDef)\n (errors : List ErrorDef) :\n ∀ (entries : List (FunctionSpec × Nat)) irFns,\n (entries.mapM fun (entry : FunctionSpec × Nat)... | [
{
"name": "compile_ok_yields_compiled_functions_with_scalar_events",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 24,
"n_chars": 965,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
... | 4 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -28,6 +28,37 @@
have ih' := ih hrest
simpa [pickUniqueFunctionByName, hfn] using ih'
+private theorem compiled_functions_forall₂_of_mapM_ok
+ (fields : List Field)
+ (events : List EventDef)
+ (errors : List ErrorDef) :
+ ∀ (entries : List (FunctionSpec × Nat)) irFns,
+ (entries.mapM... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_9 | 7c0c1d3c246865f8 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compile_ok_yields_internalFunctions_nil",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 20,
"n_chars": 718,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
"automation_only... | 4 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -72,6 +72,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.functio... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_10 | aa2edda7964b2633 | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compile_ok_yields_deploy_compileConstructor",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 21,
"n_chars": 807,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
"automation_... | 4 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -72,6 +72,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.functio... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
ablate_0b77e08220fe_11 | 925ec05cd79bcfec | lean | lean | github.com/lfglabs-dev/verity | eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978 | Compiler/Proofs/IRGeneration/ContractShape.lean | ContractShape | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "compileValidatedCore_ok_yields_compiled_functions",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfallback :\n pickUniqueFunctionByName \"fallback\" model.functions = Except.o... | [
{
"name": "supportedSpec_entries_lock_free",
"text": "theorem supportedSpec_entries_lock_free\n {model : CompilationModel} {selectors : List Nat}\n (hSupported : SupportedSpec model selectors) :\n ∀ e ∈ (model.functions.filter\n (fun fn => !fn.isInternal && !isInteropEntrypointName fn.name))... | [
{
"name": "compile_ok_yields_noFallbackEntrypoint",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 20,
"n_chars": 719,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
"automation_only"... | 4 | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | import Compiler.Proofs.IRGeneration.SourceSemantics
set_option linter.unnecessarySimpa false
namespace Compiler.Proofs.IRGeneration
open Compiler
open Compiler.CompilationModel
namespace ContractShape
private theorem pickUniqueFunctionByName_eq_ok_none_of_absent
(name : String) (funcs : List FunctionSpec)
... | @@ -72,6 +72,16 @@
compileGuardedFunctionSpec_eq_of_none fields events errors adtTypes internalFunctions e.2 e.1 hhead,
htail]
+theorem supportedSpec_entries_lock_free
+ {model : CompilationModel} {selectors : List Nat}
+ (hSupported : SupportedSpec model selectors) :
+ ∀ e ∈ (model.functio... | {
"repo": "verity",
"git_repo": "github.com/lfglabs-dev/verity",
"revision": "eeb7a3abe85dd88cc8ee2ece5a77da9b2aba2978",
"lean_toolchain": "leanprover/lean4:v4.22.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemm... |
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